Rocky Mountain Journal of Mathematics Articles (Project Euclid)
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The latest articles from Rocky Mountain Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.enusCopyright 2010 Cornell University LibraryEuclidL@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTMon, 02 May 2011 10:11 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Rings Over which All Modules are Strongly Gorenstein Projective
http://projecteuclid.org/euclid.rmjm/1277385512
<strong>Driss Bennis</strong>, <strong>Najib Mahdoua</strong>, <strong>Khalid Ouarghi</strong><p><strong>Source: </strong>Rocky Mountain J. Math., Volume 40, Number 3, 749759.</p>projecteuclid.org/euclid.rmjm/1277385512_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTReal zeros of random trigonometric polynomials with pairwise equal blocks of coefficientshttps://projecteuclid.org/euclid.rmjm/1580461724<strong> Pirhadi</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461724_20200131040853Fri, 31 Jan 2020 04:08 ESTWavelet frames in $L^2(\RR^d)$https://projecteuclid.org/euclid.rmjm/1572836560<strong> Poumai, Kaushik</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836560_20200131040853Fri, 31 Jan 2020 04:08 ESTDown the Large Rabbit Holehttps://projecteuclid.org/euclid.rmjm/1567238429<strong> Robertson</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1567238429_20200131040853Fri, 31 Jan 2020 04:08 ESTAlternative summation orders for the Eisenstein series G_2 and Weierstrass ?functionhttps://projecteuclid.org/euclid.rmjm/1580461725<strong> Romik, Scherer</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461725_20200131040853Fri, 31 Jan 2020 04:08 ESTEquivariant $K$theory of divisive torus orbifoldshttps://projecteuclid.org/euclid.rmjm/1567238430<strong> Sarkar</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1567238430_20200131040853Fri, 31 Jan 2020 04:08 ESTClosed neighborhood ideal of a graphhttps://projecteuclid.org/euclid.rmjm/1580461726<strong> Sharifan, Moradi</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461726_20200131040853Fri, 31 Jan 2020 04:08 ESTMean Lipschitz conditions and growth of area integral means of functions in Bergman spaces with an admissible Bekolle weighthttps://projecteuclid.org/euclid.rmjm/1572836561<strong> Sharma, Ueki</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836561_20200131040853Fri, 31 Jan 2020 04:08 ESTA note around operator Bellman inequalityhttps://projecteuclid.org/euclid.rmjm/1580461727<strong> Sheybani, Omidvar, Khanehgir</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461727_20200131040853Fri, 31 Jan 2020 04:08 ESTNonlinear $\ast$Jordan triple derivation on prime $\ast$algebrashttps://projecteuclid.org/euclid.rmjm/1568858425<strong> TaghaviJelodar, Nouri, Razeghi, Darvish</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1568858425_20200131040853Fri, 31 Jan 2020 04:08 ESTOn the socle of a commutative ring and Zariski topologyhttps://projecteuclid.org/euclid.rmjm/1567238431<strong> Taherifar</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1567238431_20200131040853Fri, 31 Jan 2020 04:08 ESTA remark on entropies of noncompact systemshttps://projecteuclid.org/euclid.rmjm/1576227841<strong> Tang, Li</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1576227841_20200131040853Fri, 31 Jan 2020 04:08 ESTCharacterization and enumeration of palindromic numbers whose squares are also palindromichttps://projecteuclid.org/euclid.rmjm/1580461728<strong> Tripathi</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461728_20200131040853Fri, 31 Jan 2020 04:08 ESTQuartic fields with large class numbershttps://projecteuclid.org/euclid.rmjm/1564020078<strong> Umegaki, UmegakiIchihara</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1564020078_20200131040853Fri, 31 Jan 2020 04:08 ESTTopological Ktheory with coefficients and the einvarianthttps://projecteuclid.org/euclid.rmjm/1572836564<strong> Wang</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836564_20200131040853Fri, 31 Jan 2020 04:08 ESTMeromorphic solutions of two certain types of nonlinear differential equationshttps://projecteuclid.org/euclid.rmjm/1572836565<strong> Wang, Chen, Yuan</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836565_20200131040853Fri, 31 Jan 2020 04:08 ESTBreathers, lumps and hybrid solutions of the (2+1)dimensional HirotaSatsumaIto equationhttps://projecteuclid.org/euclid.rmjm/1572836566<strong> Yang, Zhang, Li, Li</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836566_20200131040853Fri, 31 Jan 2020 04:08 ESTGround state solutions for the periodic fractional SchrodingerPoisson systems with critical Sobolev exponethttps://projecteuclid.org/euclid.rmjm/1580461729<strong> Yu, Chen, Xie</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461729_20200131040853Fri, 31 Jan 2020 04:08 ESTThe 2fold Bailey lemma and mock theta functionshttps://projecteuclid.org/euclid.rmjm/1580461730<strong> Zhang, Song</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461730_20200131040853Fri, 31 Jan 2020 04:08 ESTIrreducible convergence in $T_0$ spaceshttps://projecteuclid.org/euclid.rmjm/1567238434<strong> Zhao, Lu, Wang</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1567238434_20200131040853Fri, 31 Jan 2020 04:08 ESTLocal strong solutions to the Cauchy problem of twodimensional densitydependent Benard system with nonnegative densityhttps://projecteuclid.org/euclid.rmjm/1580461731<strong> Zhong</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461731_20200131040853Fri, 31 Jan 2020 04:08 ESTExistence and uniqueness of monotone positive solutions for fractional higher order BVPshttps://projecteuclid.org/euclid.rmjm/1572836569<strong> Zhou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836569_20200131040853Fri, 31 Jan 2020 04:08 ESTFujita exponent for a inhomogeneous pseudoparabolic equationhttps://projecteuclid.org/euclid.rmjm/1580461732<strong> Zhou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1580461732_20200131040853Fri, 31 Jan 2020 04:08 ESTEkedahlOort strata on the moduli space of curves of genus fourhttps://projecteuclid.org/euclid.rmjm/1572836570<strong> Zhou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1572836570_20200131040853Fri, 31 Jan 2020 04:08 ESTWaringGoldbach Problem: Two Squares and Three Biquadrateshttps://projecteuclid.org/euclid.rmjm/1567238435<strong> Zhu</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1567238435_20200131040853Fri, 31 Jan 2020 04:08 ESTDependence of eigenvalues of fourth order boundary value problems with transmission conditionshttps://projecteuclid.org/euclid.rmjm/1567238436<strong> Zinsou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Forthcoming articles, .</p>projecteuclid.org/euclid.rmjm/1567238436_20200131040853Fri, 31 Jan 2020 04:08 ESTMinimal index of bicyclic biquadratic number fieldshttps://projecteuclid.org/euclid.rmjm/1588233620<strong>Tímea Arnóczki</strong>, <strong>Gábor Nyul</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 18.</p><p><strong>Abstract:</strong><br/>
T. Nakahara proved that the set of minimal indices of bicyclic biquadratic number fields with field index [math] is unbounded. We strengthen his result by showing that this set just coincides with the set of positive integers, and every positive integer occurs infinitely many times as minimal index of totally complex bicyclic biquadratic number fields. Moreover, we study the analogous problem for all the other possible values of the field index.
</p>projecteuclid.org/euclid.rmjm/1588233620_20200430040042Thu, 30 Apr 2020 04:00 EDTA new approach to the automorphism group of a platonic surfacehttps://projecteuclid.org/euclid.rmjm/1588233623<strong>David Aulicino</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 923.</p><p><strong>Abstract:</strong><br/>
We borrow a classical construction from the study of rational billiards in dynamical systems known as the “unfolding construction” and show that it can be used to study the automorphism group of a Platonic surface. More precisely, the monodromy group, or deck group in this case, associated to the cover of a regular polygon or double polygon by the unfolded Platonic surface yields a normal subgroup of the rotation group of the Platonic surface. The quotient of this rotation group by the normal subgroup is always a cyclic group, where explicit bounds on the order of the cyclic group can be given entirely in terms of the Schläfli symbol of the Platonic surface. As a consequence, we provide a new derivation of the rotation groups of the dodecahedron and the Bolza surface.
</p>projecteuclid.org/euclid.rmjm/1588233623_20200430040042Thu, 30 Apr 2020 04:00 EDTApollonian sets in taxicab geometryhttps://projecteuclid.org/euclid.rmjm/1588233628<strong>Eric Bahuaud</strong>, <strong>Shana Crawford</strong>, <strong>Aaron Fish</strong>, <strong>Dylan Helliwell</strong>, <strong>Anna Miller</strong>, <strong>Freddy Nungaray</strong>, <strong>Suki Shergill</strong>, <strong>Julian Tiffay</strong>, <strong>Nico Velez</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 2539.</p><p><strong>Abstract:</strong><br/>
Fix two points [math] and [math] in the plane and a positive number [math] . A result credited to Apollonius of Perga states that the set of points [math] that satisfy [math] forms a circle. In this paper we study the analogous set in taxicab geometry. We find that while Apollonian sets are not taxicab circles, more complicated Apollonian sets can be characterized in terms of simpler ones.
</p>projecteuclid.org/euclid.rmjm/1588233628_20200430040042Thu, 30 Apr 2020 04:00 EDTSolitons and geometrical structures in a perfect fluid spacetimehttps://projecteuclid.org/euclid.rmjm/1588233629<strong>Adara M. Blaga</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 4153.</p><p><strong>Abstract:</strong><br/>
Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and [math] Ricci and [math] Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector field [math] of the soliton is of gradient type, [math] , we derive a Poisson equation from the soliton equation.
</p>projecteuclid.org/euclid.rmjm/1588233629_20200430040042Thu, 30 Apr 2020 04:00 EDTConvergence of solutions for Fisher–KPP equation with a free boundary conditionhttps://projecteuclid.org/euclid.rmjm/1588233630<strong>Jingjing Cai</strong>, <strong>Yuan Chai</strong>, <strong>Qiong Liu</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 5568.</p><p><strong>Abstract:</strong><br/>
We consider a free boundary problem: [math] ( [math] ) with free boundary conditions [math] and [math] , where [math] is a positive [math] periodic function, [math] is a Fisher–KPP type of nonlinearity and [math] periodic in [math] . Such a problem can model the spreading of a biological or chemical species in timeperiodic environment, where free boundaries mimic the spreading fronts of the species. We mainly study the convergence of bounded solutions. There is a [math] periodic function [math] which plays a key role in the dynamics. More precisely:
(i) When [math] , we obtain a trichotomy result:
Spreading, i.e.,
[math]
and
[math]
as
[math] ,
where
[math]
is the periodic solution of the ODE
[math] .
Vanishing, i.e.,
[math]
and
[math] ,
where
[math]
is some positive constant.
Transition, i.e.,
[math] ,
[math]
and
[math] ,
where
[math]
is a
[math] periodic
solution with compact support.
(ii) In the case [math] , vanishing happens for any solution.
</p>projecteuclid.org/euclid.rmjm/1588233630_20200430040042Thu, 30 Apr 2020 04:00 EDTBiHomalternative, BiHomMalcev and BiHomJordan algebrashttps://projecteuclid.org/euclid.rmjm/1588233631<strong>Taoufik Chtioui</strong>, <strong>Sami Mabrouk</strong>, <strong>Abdenacer Makhlouf</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 6990.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to introduce and study BiHomalternative algebras and BiHomMalcev algebras. It is shown that BiHomalternative algebras are BiHomMalcev admissible and BiHomJordan admissible. Moreover, BiHomtype generalizations of some well known identities in alternative algebras, including the Moufang identities, are obtained.
</p>projecteuclid.org/euclid.rmjm/1588233631_20200430040042Thu, 30 Apr 2020 04:00 EDTElliptic operators and Khomologyhttps://projecteuclid.org/euclid.rmjm/1588233632<strong>Anna Duwenig</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 91124.</p><p><strong>Abstract:</strong><br/>
If a differential operator [math] on a smooth Hermitian vector bundle [math] over a compact manifold [math] is symmetric, it is essentially selfadjoint and so admits the use of functional calculus. If [math] is also elliptic, then the Hilbert space of square integrable sections of [math] with the canonical left [math] action and the operator [math] for [math] a normalizing function is a Fredholm module, and its [math] homology class is independent of [math] . In this expository article, we provide a detailed proof of this fact following the outline in the book “Analytic Khomology” by Higson and Roe.
</p>projecteuclid.org/euclid.rmjm/1588233632_20200430040042Thu, 30 Apr 2020 04:00 EDTTangential approximation of analytic setshttps://projecteuclid.org/euclid.rmjm/1588233633<strong>Massimo Ferrarotti</strong>, <strong>Elisabetta Fortuna</strong>, <strong>Leslie Wilson</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 125133.</p><p><strong>Abstract:</strong><br/>
Two subanalytic subsets of [math] are called [math] equivalent at a common point [math] if the Hausdorff distance between their intersections with the sphere centered at [math] of radius [math] vanishes to order [math] as [math] tends to [math] . We strengthen this notion in the case of real subanalytic subsets of [math] with isolated singular points, introducing the notion of tangential [math] equivalence at a common singular point, which considers also the distance between the tangent planes to the sets near the point. We prove that, if [math] is the zero set of an analytic map [math] and if we assume that [math] has an isolated singularity, say at the origin [math] , then for any [math] the truncation of the Taylor series of [math] of sufficiently high order defines an algebraic set with isolated singularity at [math] which is tangentially [math] equivalent to [math] .
</p>projecteuclid.org/euclid.rmjm/1588233633_20200430040042Thu, 30 Apr 2020 04:00 EDTCombinatorics of $k$Farey graphshttps://projecteuclid.org/euclid.rmjm/1588233634<strong>Jonah Gaster</strong>, <strong>Miguel Lopez</strong>, <strong>Emily Rexer</strong>, <strong>Zoë Riell</strong>, <strong>Yang Xiao</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 135151.</p><p><strong>Abstract:</strong><br/>
With an eye towards studying curve systems on lowcomplexity surfaces, we introduce and analyze the [math] Farey graphs [math] and [math] , two natural variants of the Farey graph [math] in which we relax the edge condition to indicate intersection number [math] or [math] , respectively.
The former, [math] , is disconnected when [math] . In fact, we find that the number of connected components is infinite if and only if [math] is not a prime power. Moreover, we find that each component of [math] is a quasitree (in fact, a tree when [math] is even) and [math] is uncountable for [math] .
As for [math] , Agol obtained an upper bound of [math] for both chromatic and clique numbers, and observed that this is an equality when [math] is either one or two less than a prime. We add to this list the values of [math] that are three less than a prime equivalent to [math] , and we show computerassisted computations of many values of [math] for which equality fails.
</p>projecteuclid.org/euclid.rmjm/1588233634_20200430040042Thu, 30 Apr 2020 04:00 EDTGroups whose proper subgroups are metahamiltonianbyfinitehttps://projecteuclid.org/euclid.rmjm/1588233635<strong>Francesco de Giovanni</strong>, <strong>Marco Trombetti</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 153162.</p><p><strong>Abstract:</strong><br/>
A group is called metahamiltonian if all its nonabelian subgroups are normal. It is known that any infinite locally graded group whose proper subgroups are metahamiltonian is likewise metahamiltonian, and the aim of this paper is to describe the structure of locally graded groups whose proper subgroups contain a metahamiltonian subgroup of finite index.
</p>projecteuclid.org/euclid.rmjm/1588233635_20200430040042Thu, 30 Apr 2020 04:00 EDTLietype derivations of finitary incidence algebrashttps://projecteuclid.org/euclid.rmjm/1588233636<strong>Mykola Khrypchenko</strong>, <strong>Feng Wei</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 163175.</p><p><strong>Abstract:</strong><br/>
Let [math] be an arbitrary partially ordered set, [math] be a commutative ring with identity and [math] be the finitary incidence algebra of [math] over [math] . Under some natural assumption on [math] , we prove that each Lietype derivation of [math] is proper, which partially generalizes the main results of Zhang and Khrypchenko (2017), Wang and Xiao (2019), and Xiao and Yang (2019).
</p>projecteuclid.org/euclid.rmjm/1588233636_20200430040042Thu, 30 Apr 2020 04:00 EDTThree open questions on residually small ringshttps://projecteuclid.org/euclid.rmjm/1588233637<strong>Rahul Kumar</strong>, <strong>Atul Gaur</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 177180.</p><p><strong>Abstract:</strong><br/>
Recently in 2018, four open questions were raised by Oman and Salminen (2018). We answer three of them in this article.
</p>projecteuclid.org/euclid.rmjm/1588233637_20200430040042Thu, 30 Apr 2020 04:00 EDTFrom the signature theorem to anomaly cancellationhttps://projecteuclid.org/euclid.rmjm/1588233638<strong>Andreas Malmendier</strong>, <strong>Michael T. Schultz</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 181212.</p><p><strong>Abstract:</strong><br/>
We survey the Hirzebruch signature theorem as a special case of the Atiyah–Singer index theorem. The family version of the Atiyah–Singer index theorem in the form of the Riemann–Roch–Grothendieck–Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula allows us to determine a generalized cohomology class on the base of the elliptic fibration that is known in physics as (a measure of) the local and global anomaly. Combining several anomalous operators allows us to cancel the local anomaly on a Jacobian elliptic surface, a construction that is based on the construction of the Poincaré line bundle over an elliptic surface.
</p>projecteuclid.org/euclid.rmjm/1588233638_20200430040042Thu, 30 Apr 2020 04:00 EDTOn von Neumann's inequality for complex triangular Toeplitz contractionshttps://projecteuclid.org/euclid.rmjm/1588233639<strong>Joachim Moussounda Mouanda</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 213224.</p><p><strong>Abstract:</strong><br/>
We prove that von Neumann’s inequality holds for circulant contractions. We show that every complex polynomial [math] over [math] is associated to a constant [math] such that von Neumann’s inequality can hold up to [math] , for [math] tuples of commuting contractions on a Hilbert space. We characterise complex polynomials over [math] in which [math] . We introduce the properties of upper (or lower) complex triangular Toeplitz matrices. We show that von Neumann’s inequality holds for [math] tuples of upper (or lower) complex triangular Toeplitz contractions. We construct contractive homomorphisms.
</p>projecteuclid.org/euclid.rmjm/1588233639_20200430040042Thu, 30 Apr 2020 04:00 EDTOn sum formulas for Mordell–Tornheim zeta valueshttps://projecteuclid.org/euclid.rmjm/1588233640<strong>Maneka Pallewatta</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 225235.</p><p><strong>Abstract:</strong><br/>
In this paper we prove new sum formulas for Mordell–Tornheim zeta values in the case of depth 2 and 3, expressing the sums as single multiples of Riemann zeta values. Also, we obtain weighted sum formulas for double Mordell–Tornheim zeta values. Moreover, we present a sum formula for the Mordell–Tornheim series of even arguments.
</p>projecteuclid.org/euclid.rmjm/1588233640_20200430040042Thu, 30 Apr 2020 04:00 EDTDown the large rabbit holehttps://projecteuclid.org/euclid.rmjm/1588233641<strong>Aaron Robertson</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 237253.</p><p><strong>Abstract:</strong><br/>
This article documents my journey down the rabbit hole, chasing what I have come to know as a particularly unyielding problem in Ramsey theory on the integers: the [math] large conjecture. This conjecture states that if [math] has the property that every [math] coloring of [math] admits arbitrarily long monochromatic arithmetic progressions with common difference from [math] , then the same property holds for any finite number of colors. We hope to provide a roadmap for future researchers and also provide some new results related to the [math] large conjecture.
</p>projecteuclid.org/euclid.rmjm/1588233641_20200430040042Thu, 30 Apr 2020 04:00 EDTEquivariant $K$theory of divisive torus orbifoldshttps://projecteuclid.org/euclid.rmjm/1588233642<strong>Soumen Sarkar</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 255266.</p><p><strong>Abstract:</strong><br/>
The category of torus orbifolds is a generalization of the category of toric orbifolds which contains projective toric varieties associated to complete simplicial fans. We introduce the concept of “divisive” torus orbifolds following divisive weighted projective spaces. The divisive condition may ensure an invariant cell structure on a locally standard torus orbifold. We give a combinatorial description of equivariant [math] theory, equivariant cobordism theory and equivariant cohomology theory of divisive torus orbifolds. In particular, we get a combinatorial description of these generalize cohomology theories for torus manifolds over acyclic polytopes.
</p>projecteuclid.org/euclid.rmjm/1588233642_20200430040042Thu, 30 Apr 2020 04:00 EDTQuartic fields with large class numbershttps://projecteuclid.org/euclid.rmjm/1588233643<strong>Atsuki Umegaki</strong>, <strong>Yumiko Umegaki</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 267280.</p><p><strong>Abstract:</strong><br/>
We show that there exist infinitely many quartic number fields [math] with large class numbers such that [math] is a Galois extension whose Galois group is isomorphic to a given finite group. Cho and Kim proved that there are infinitely many totally real cyclic extensions over [math] of degree [math] with large class numbers. We consider all the other cases of quartic Galois extensions.
</p>projecteuclid.org/euclid.rmjm/1588233643_20200430040042Thu, 30 Apr 2020 04:00 EDTTopological $K$theory with coefficients and the $e$invarianthttps://projecteuclid.org/euclid.rmjm/1588233644<strong>YiSheng Wang</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 281318.</p><p><strong>Abstract:</strong><br/>
We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map from the [math] connective algebraic [math] theory space of the complex numbers to the homotopy fiber of the Chern character. We examine homotopy properties of this map and its relation with other known invariants. In addition, using the formula for [math] invariants of lens spaces derived from Donnelly’s fixed point theorem and the [math] dimensional cobordisms constructed via relative Kirby diagrams, we recover the formula of the [math] invariants of Seifert homology spheres given by Jones and Westbury, up to sign.
</p>projecteuclid.org/euclid.rmjm/1588233644_20200430040042Thu, 30 Apr 2020 04:00 EDTBreathers, lumps and hybrid solutions of the $(2{+}1)$dimensional Hirota–Satsuma–Ito equationhttps://projecteuclid.org/euclid.rmjm/1588233645<strong>Xiangyu Yang</strong>, <strong>Zhao Zhang</strong>, <strong>Wentao Li</strong>, <strong>Biao Li</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 319335.</p><p><strong>Abstract:</strong><br/>
With the Hirota bilinear method and symbolic computation, explicit forms of [math] soliton of the [math] dimensional Hirota–Satsuma–Ito equation are derived. General highorder breather solutions are constructed through appropriate parameter restrictions. By performing an appropriate limiting procedures on soliton solutions and then making further parameter constraints, general lump solutions to the [math] dimensional Hirota–Satsuma–Ito equation would be succinctly constructed. Furthermore, we provide the hybrid solutions which means different types of combinations in breathers, lumps and line solitons. In order to better understand the dynamical behaviors of the equation, the novel interaction and propagation characteristics are discussed graphically.
</p>projecteuclid.org/euclid.rmjm/1588233645_20200430040042Thu, 30 Apr 2020 04:00 EDTIrreducible convergence in $T_0$ spaceshttps://projecteuclid.org/euclid.rmjm/1588233646<strong>Bin Zhao</strong>, <strong>Jing Lu</strong>, <strong>Kaiyun Wang</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 337353.</p><p><strong>Abstract:</strong><br/>
In this paper, we define and study irreducible convergence and irreducible orderconvergence in [math] spaces, which can be seen as topological counterparts of liminfconvergence and orderconvergence in posets, respectively. Especially, we give sufficient and necessary conditions for irreducible convergence and irreducible orderconvergence in [math] spaces to be topological.
</p>projecteuclid.org/euclid.rmjm/1588233646_20200430040042Thu, 30 Apr 2020 04:00 EDTWaring–Goldbach problem: two squares and three biquadrateshttps://projecteuclid.org/euclid.rmjm/1588233647<strong>Li Zhu</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 355367.</p><p><strong>Abstract:</strong><br/>
Let [math] denote the number of representations of the positive integer [math] as the sum of two squares and three biquadrates of primes and we write [math] for the number of positive integers [math] satisfying [math] , [math] and

ℛ
(
n
)
−
Γ
2
(
1
2
)
Γ
3
(
1
4
)
Γ
(
7
4
)
𝔖
(
n
)
n
3
4
log
5
n

≥
n
3
4
log
1
1
2
n
,
where [math] is the singular series. In this paper, we prove
ℰ
(
N
)
≪
N
1
5
3
2
+
𝜀
for any [math] . This result constitutes a refinement upon that of Friedlander and Wooley (2014).
</p>projecteuclid.org/euclid.rmjm/1588233647_20200430040042Thu, 30 Apr 2020 04:00 EDTDependence of eigenvalues of fourthorder boundary value problems with transmission conditionshttps://projecteuclid.org/euclid.rmjm/1588233648<strong>Bertin Zinsou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 1, 369382.</p><p><strong>Abstract:</strong><br/>
A general fourthorder regular ordinary differential equation with eigenvalue dependent boundary conditions and transmission conditions are considered. We prove that the eigenvalues depend continuously and smoothly on the coefficients of the differential equation and on the boundary and transmission matrices. We provide as well formulas for the derivatives with respect to each of these parameters.
</p>projecteuclid.org/euclid.rmjm/1588233648_20200430040042Thu, 30 Apr 2020 04:00 EDTRigidity and flatness of the image of certain classes of mappings having tangential Laplacianhttps://projecteuclid.org/euclid.rmjm/1590739277<strong>Hussien Abugirda</strong>, <strong>Birzhan Ayanbayev</strong>, <strong>Nikos Katzourakis</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 383396.</p><p><strong>Abstract:</strong><br/>
In this paper we consider the PDE system of vanishing normal projection of the Laplacian for [math] maps [math] :
[
[
D
u
]
]
⊥
Δ
u
=
0
in
Ω
.
This system has discontinuous coefficients and geometrically expresses the fact that the Laplacian is a vector field tangential to the image of the mapping. It arises as a constituent component of the [math] Laplace system for all [math] . For [math] , the [math] Laplace system is the archetypal equation describing extrema of supremal functionals in vectorial calculus of variations in [math] . Herein we show that the image of a solution [math] is piecewise affine if either the rank of [math] is equal to one or [math] and [math] has additively separated form. As a consequence we obtain corresponding flatness results for [math] Harmonic maps for [math] .
</p>projecteuclid.org/euclid.rmjm/1590739277_20200529040131Fri, 29 May 2020 04:01 EDTMultidimensional scaling on metric measure spaceshttps://projecteuclid.org/euclid.rmjm/1590739278<strong>Henry Adams</strong>, <strong>Mark Blumstein</strong>, <strong>Lara Kassab</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 397413.</p><p><strong>Abstract:</strong><br/>
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a lowdimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its optimality properties and goodness of fit. Further, we present a notion of MDS on infinite metric measure spaces that generalizes these optimality properties. As a consequence we can study the MDS embeddings of the geodesic circle [math] into [math] for all [math] , and ask questions about the MDS embeddings of the geodesic [math] spheres [math] into [math] . Finally, we address questions on convergence of MDS. For instance, if a sequence of metric measure spaces converges to a fixed metric measure space [math] , then in what sense do the MDS embeddings of these spaces converge to the MDS embedding of [math] ?
</p>projecteuclid.org/euclid.rmjm/1590739278_20200529040131Fri, 29 May 2020 04:01 EDTFourier transforms, fractional derivatives, and a little bit of quantum mechanicshttps://projecteuclid.org/euclid.rmjm/1590739279<strong>Fabio Bagarello</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 415428.</p><p><strong>Abstract:</strong><br/>
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions [math] , and then we extend it to its dual set, [math] , the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.
</p>projecteuclid.org/euclid.rmjm/1590739279_20200529040131Fri, 29 May 2020 04:01 EDTAsymptotic order statistics of mixtures of distributionshttps://projecteuclid.org/euclid.rmjm/1590739280<strong>Haroon M. Barakat</strong>, <strong>Mohamed A. Abd Elgawad</strong>, <strong>Metwally A. Alawady</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 429443.</p><p><strong>Abstract:</strong><br/>
We study the asymptotic distribution of the linearly normalized extremes under finite mixture models. Moreover, the asymptotic distributions of the generally normalized central and intermediate order statistics under finite mixture models are studied.
</p>projecteuclid.org/euclid.rmjm/1590739280_20200529040131Fri, 29 May 2020 04:01 EDTExistence of positive solutions for a new class of Kirchhoff parabolic systemshttps://projecteuclid.org/euclid.rmjm/1590739281<strong>Salah Boulaaras</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 445454.</p><p><strong>Abstract:</strong><br/>
We study the existence of weak positive solutions for a new class of Kirchhoff parabolic systems in bounded domains with multiple parameters taking into account the symmetry conditions and the righthand side defined as a multiplication of two separate functions. Our results are natural extensions of previous results in the field, which used the same method for some classical elliptic equations.
</p>projecteuclid.org/euclid.rmjm/1590739281_20200529040131Fri, 29 May 2020 04:01 EDTSome inequalities for weighted area balance via functions of bounded variationhttps://projecteuclid.org/euclid.rmjm/1590739282<strong>Hüseyin Budak</strong>, <strong>Ebru Pehlivan</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 455466.</p><p><strong>Abstract:</strong><br/>
We first define weighted area balance function. Then we prove two identities for the integrable functions involving weighted area balance. Moreover, using these equalities, we obtain some inequalities for mappings of bounded variation and for Lipschitzian functions, respectively.
</p>projecteuclid.org/euclid.rmjm/1590739282_20200529040131Fri, 29 May 2020 04:01 EDTSets with countably infinitely many prescribed weighted densitieshttps://projecteuclid.org/euclid.rmjm/1590739283<strong>József Bukor</strong>, <strong>Ferdinánd Filip</strong>, <strong>János T. Tóth</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 467477.</p><p><strong>Abstract:</strong><br/>
It is known that there exist classes of sets of positive integers which provide arbitrary given values as lower and upper logarithmic and asymptotic densities. The only restriction is the inequality between these densities. We generalize this result for a sequence of weighted densities, i.e., for countably infinitely many weighted densities.
</p>projecteuclid.org/euclid.rmjm/1590739283_20200529040131Fri, 29 May 2020 04:01 EDTMeromorphic solutions of two certain types of nonlinear differential equationshttps://projecteuclid.org/euclid.rmjm/1590739284<strong>Wei Chen</strong>, <strong>Qiong Wang</strong>, <strong>Wenjun Yuan</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 479497.</p><p><strong>Abstract:</strong><br/>
We investigate the meromorphic solutions of two types of nonlinear differential equations of the form
[math]
where [math] are constants with [math] and [math] are positive integers, [math] are nonzero rational functions, [math] are nonconstant polynomials, and [math] denotes a differential polynomial in [math] with rational functions as its coefficients. Our results improve some recent related results.
</p>projecteuclid.org/euclid.rmjm/1590739284_20200529040131Fri, 29 May 2020 04:01 EDTOn sets with more products than quotientshttps://projecteuclid.org/euclid.rmjm/1590739285<strong>Hùng Việt Chu</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 499512.</p><p><strong>Abstract:</strong><br/>
Given a finite set [math] , define
A
⋅
A
=
{
a
i
⋅
a
j
∣
a
i
,
a
j
∈
A
}
,
A
∕
A
=
{
a
i
∕
a
j
∣
a
i
,
a
j
∈
A
}
,
A
+
A
=
{
a
i
+
a
j
∣
a
i
,
a
j
∈
A
}
,
A
−
A
=
{
a
i
−
a
j
∣
a
i
,
a
j
∈
A
}
.
The set [math] is said to be MPTQ (more product than quotient) if [math] and MSTD (more sum than difference) if [math] . Since multiplication and addition are commutative while division and subtraction are not, it is natural to think that MPTQ and MSTD sets are very rare. However, they do exist. This paper first shows an efficient search for MPTQ subsets of [math] and proves that as [math] , the proportion of MPTQ subsets approaches [math] . Next, we prove that MPTQ sets of positive numbers must have at least [math] elements, while MPTQ sets of both negative and positive numbers must have at least [math] elements. Finally, we investigate several sequences that do not have MPTQ subsets.
</p>projecteuclid.org/euclid.rmjm/1590739285_20200529040131Fri, 29 May 2020 04:01 EDTCongruences for $\ell$regular partitions and bipartitionshttps://projecteuclid.org/euclid.rmjm/1590739286<strong>SuPing Cui</strong>, <strong>Nancy S. S. Gu</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 513526.</p><p><strong>Abstract:</strong><br/>
Define [math] , which includes Ramanujan’s theta function as a special case. We establish a dissection identity for this function, and use it to derive congruence properties for the coefficients of [math] . As an application we deduce several infinite families of congruences for [math] regular partitions and [math] regular bipartitions. In addition, we give a new proof of Ramanujan’s congruence for the unrestricted partition function modulo [math] .
</p>projecteuclid.org/euclid.rmjm/1590739286_20200529040131Fri, 29 May 2020 04:01 EDTExistence of global solutions for a weakly coupled system of semilinear viscoelastic damped $\sigma$evolution equationshttps://projecteuclid.org/euclid.rmjm/1590739287<strong>Tuan Anh Dao</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 527542.</p><p><strong>Abstract:</strong><br/>
We prove the global (in time) existence of small data solutions from energy spaces based on [math] spaces, [math] , to the Cauchy problem for a weakly coupled system of semilinear viscoelastic damped [math] evolution equations, where we consider nonlinearity terms with powers [math] and any [math] in the comparison between two single equations. To do this, by mixing additional [math] regularity for the data on the basis of [math]  [math] estimates, with [math] and [math] , we apply [math]  [math] estimates for solutions to the corresponding linear Cauchy problems to treat semilinear problems. In addition, two different strategies allowing no loss of decay and some loss of decay combined with the flexible choice of admissible parameters [math] , [math] , [math] and [math] bring some benefits to relax the restrictions on the admissible exponents [math] .
</p>projecteuclid.org/euclid.rmjm/1590739287_20200529040131Fri, 29 May 2020 04:01 EDTNonlinear $\ast$Jordan triple derivation on prime $\ast$algebrashttps://projecteuclid.org/euclid.rmjm/1590739288<strong>Vahid Darvish</strong>, <strong>Mojtaba Nouri</strong>, <strong>Mehran Razeghi</strong>, <strong>Ali Taghavi</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 543549.</p><p><strong>Abstract:</strong><br/>
Let [math] be a prime [math] algebra and suppose that [math] preserves triple [math] Jordan derivation on [math] , that is, for every [math] ,
Φ
(
A
◇
B
◇
C
)
=
Φ
(
A
)
◇
B
◇
C
+
A
◇
Φ
(
B
)
◇
C
+
A
◇
B
◇
Φ
(
C
)
,
where [math] . Then [math] is additive. Moreover, if [math] is selfadjoint for [math] , then [math] is a [math] derivation.
</p>projecteuclid.org/euclid.rmjm/1590739288_20200529040131Fri, 29 May 2020 04:01 EDTA decomposition of $\zeta(2n+3)$ into sums of multiple zeta valueshttps://projecteuclid.org/euclid.rmjm/1590739289<strong>Minking Eie</strong>, <strong>WenChin Liaw</strong>, <strong>Yao Lin Ong</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 551558.</p><p><strong>Abstract:</strong><br/>
We evaluate the multiple zeta value [math] or its dual [math] . When [math] is even, along with stuffle relations already available, it is enough to evaluate all multiple zeta values of the form [math] with [math] . Furthermore, we obtain a decomposition for [math] as
ζ
⋆
(
3
,
{
2
}
n
)
+
ζ
(
{
2
}
n
,
3
)
+
∑
r
=
1
n
∑

α

=
n
+
1
ζ
(
1
,
2
α
1
,
2
α
2
,
…
,
2
α
r
)
,
which also can be used to evaluate [math] when [math] is even.
</p>projecteuclid.org/euclid.rmjm/1590739289_20200529040131Fri, 29 May 2020 04:01 EDTSome control problems for the Burgers equationhttps://projecteuclid.org/euclid.rmjm/1590739290<strong>Peng Gao</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 559581.</p><p><strong>Abstract:</strong><br/>
We show the existence of insensitizing controls and study null controllability with constraints for the Burgers equation. We solve these problems by first considering the linearized problem, then, by the Kakutani fixed point theorem, we show that the same results hold for the Burgers equation. The main difficulty in this paper is dealing with the nonlinear term in the Burgers equation.
</p>projecteuclid.org/euclid.rmjm/1590739290_20200529040131Fri, 29 May 2020 04:01 EDTConservation of the number of zeros of entire functions inside and outside a circle under perturbationshttps://projecteuclid.org/euclid.rmjm/1590739291<strong>Michael Gil’</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 583588.</p><p><strong>Abstract:</strong><br/>
Let [math] and [math] be entire functions of order less than two, and [math] . Let [math] and [math] denote the numbers of the zeros of [math] taken with their multiplicities located inside and outside [math] , respectively. Besides, [math] can be infinite. We consider the following problem: how “close” should [math] and [math] be in order to provide the equalities [math] and [math] ? If for [math] we have the lower bound on the boundary, that problem sometimes can be solved by the Rouché theorem, but the calculation of such a bound is often a hard task. We do not require the lower bounds. We restrict ourselves by functions of order no more than two. Our results are new even for polynomials.
</p>projecteuclid.org/euclid.rmjm/1590739291_20200529040131Fri, 29 May 2020 04:01 EDTA dual of colored tilings terminating sumshttps://projecteuclid.org/euclid.rmjm/1590739292<strong>Matko Glunčić</strong>, <strong>Ivica Martinjak</strong>, <strong>Vladimir Paar</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 589597.</p><p><strong>Abstract:</strong><br/>
We present several enumerative identities involving thirdorder recursive sequences. In particular, we prove a dual of such identities. We also give a combinatorial interpretation of these sequences through weighted tilings and use it to find bijective proofs of presented relations.
</p>projecteuclid.org/euclid.rmjm/1590739292_20200529040131Fri, 29 May 2020 04:01 EDTOscillatory behavior of solutions of dynamic equations of higher order on time scaleshttps://projecteuclid.org/euclid.rmjm/1590739293<strong>Taher S. Hassan</strong>, <strong>Donal O’Regan</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 599617.</p><p><strong>Abstract:</strong><br/>
We study the [math] thorder nonlinear dynamic equations
x
[
n
]
(
t
)
+
p
(
t
)
ϕ
α
n
−
1
[
(
x
[
n
−
2
]
(
t
)
)
Δ
σ
]
+
q
(
t
)
ϕ
γ
(
x
(
g
(
t
)
)
)
=
0
on an unbounded time scale [math] , where [math] and for [math]
x
[
i
]
(
t
)
:
=
r
i
(
t
)
ϕ
α
i
[
(
x
[
i
−
1
]
(
t
)
)
Δ
]
,
with [math] and [math] ; here the constants [math] and the functions [math] , [math] , are positive and [math] , [math] are nonnegative functions. Criteria are established for the oscillation of solutions for both even and oddorder cases. The results improve several known results in the literature on secondorder, thirdorder, and higherorder linear and nonlinear dynamic equations. In particular our results can be applied when [math] is not (delta) differentiable and the forward jump operator [math] and [math] do not commute.
</p>projecteuclid.org/euclid.rmjm/1590739293_20200529040131Fri, 29 May 2020 04:01 EDTThe Cohen type theorem and the Eakin–Nagata type theorem for $S$Noetherian rings revisitedhttps://projecteuclid.org/euclid.rmjm/1590739294<strong>Dong Kyu Kim</strong>, <strong>Jung Wook Lim</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 619630.</p><p><strong>Abstract:</strong><br/>
We give a new proof of the Cohen type theorem for [math] Noetherian rings and a slight generalization of the Eakin–Nagata type theorem for [math] Noetherian rings.
</p>projecteuclid.org/euclid.rmjm/1590739294_20200529040131Fri, 29 May 2020 04:01 EDTApplications of Bergman representative coordinateshttps://projecteuclid.org/euclid.rmjm/1590739295<strong>Steven G. Krantz</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 631637.</p><p><strong>Abstract:</strong><br/>
We consider the representative coordinates of S. Bergman and give some applications to the study of holomorphic mappings.
</p>projecteuclid.org/euclid.rmjm/1590739295_20200529040131Fri, 29 May 2020 04:01 EDTConvergence of a class of Schrödinger equationshttps://projecteuclid.org/euclid.rmjm/1590739296<strong>Dan Li</strong>, <strong>Haixia Yu</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 639649.</p><p><strong>Abstract:</strong><br/>
We set up the selection conditions for time series [math] which converge to 0 as [math] and for which the solutions of a class of generalized Schrödinger equations pointwise converge almost everywhere to their initial data in [math] for [math] .
</p>projecteuclid.org/euclid.rmjm/1590739296_20200529040131Fri, 29 May 2020 04:01 EDTSome properties of solutions to the Riccati equations in connection with Bergman spaceshttps://projecteuclid.org/euclid.rmjm/1590739297<strong>Junming Liu</strong>, <strong>Huayou Xie</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 651657.</p><p><strong>Abstract:</strong><br/>
We investigate the properties of solutions to operator Riccati equations in connection with Bergman spaces. We characterize some necessary conditions for the solvability of the Riccati equation
X
A
X
+
X
B
−
C
X
−
D
=
0
on the set [math] of all Toeplitz operators on the Bergman spaces [math] . This extends the results of Karaev on Hardy space.
</p>projecteuclid.org/euclid.rmjm/1590739297_20200529040131Fri, 29 May 2020 04:01 EDTNew oscillation criteria for $p$Laplacian dynamic equations on time scaleshttps://projecteuclid.org/euclid.rmjm/1590739298<strong>Shekhar Singh Negi</strong>, <strong>Syed Abbas</strong>, <strong>Muslim Malik</strong>, <strong>Said R. Grace</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 659670.</p><p><strong>Abstract:</strong><br/>
We establish some new oscillation criteria of firstorder [math] Laplacian nonlinear dynamic equations on timescales. We also discuss the Kamenev and Philostype oscillation criteria. Consequently, we apply these techniques to improve and extend the results in the literature. Further, our results are demonstrated through some interesting examples.
</p>projecteuclid.org/euclid.rmjm/1590739298_20200529040131Fri, 29 May 2020 04:01 EDTUlrich bundles on some twisted flagshttps://projecteuclid.org/euclid.rmjm/1590739299<strong>Saša Novaković</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 671676.</p><p><strong>Abstract:</strong><br/>
We prove that certain twisted flag varieties carry Ulrich bundles.
</p>projecteuclid.org/euclid.rmjm/1590739299_20200529040131Fri, 29 May 2020 04:01 EDTWavelet frames in $L^2(\mathbb{R}^d)$https://projecteuclid.org/euclid.rmjm/1590739300<strong>Khole Timothy Poumai</strong>, <strong>Shiv Kumar Kaushik</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 677692.</p><p><strong>Abstract:</strong><br/>
We obtain a necessary and sufficient condition for the existence of wavelet frames. We define and study the synthesis and analysis operators associated with wavelet frames. We discuss some applications of operator value (OPV) frames in the theory of wavelet frames. Also, we discuss the minimal property of wavelet frame coefficients and study the property of over completeness of wavelet frames. Various characterizations of wavelet frame, Riesz wavelet basis and orthonormal wavelet basis are given. Further, dual wavelet frames are discussed and a characterization of dual wavelet frames is given. Finally, we give a characterization of a pair of biorthogonal Riesz bases.
</p>projecteuclid.org/euclid.rmjm/1590739300_20200529040131Fri, 29 May 2020 04:01 EDTMean Lipschitz conditions and growth of area integral means of functions in Bergman spaces with an admissible Békollé weighthttps://projecteuclid.org/euclid.rmjm/1590739301<strong>Ajay K. Sharma</strong>, <strong>Seiichiro Ueki</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 693706.</p><p><strong>Abstract:</strong><br/>
Galanopoulos et al. proved that the mean Lipschitz condition for [math] in the classical Bergman space is characterized by the growth of the area integral mean of its derivative as well as by the growth of the norm of the difference between [math] and the dilated function of [math] . We prove that functions in the weighted Bergman space with admissible Békollé weights also have the same property. Furthermore we investigate the Bloch and Zygmundtype spaces for admissible weight.
</p>projecteuclid.org/euclid.rmjm/1590739301_20200529040131Fri, 29 May 2020 04:01 EDTOn the socle of a commutative ring and Zariski topologyhttps://projecteuclid.org/euclid.rmjm/1590739302<strong>Ali Taherifar</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 707717.</p><p><strong>Abstract:</strong><br/>
This paper concerns the coincidence of the socle of a semiprimitive ring (or just a reduced one, in some cases) with the intersection of all essential prime, essential minimal prime, or essential maximal ideals of the ring. More precisely, we prove first that the socle of a reduced ring coincides with the intersection of all essential minimal prime ideals if and only if every minimal prime (or, equivalently, every prime) ideal is either essential or it is a direct summand which is also a maximal ideal. Next, we show that the socle of a semiprimitive ring [math] is equal to the intersection of all essential maximal ideals of [math] (i.e., [math] ) if and only if the set of isolated points of [math] with the Zariski topology contains no infinite basic open set. Whenever [math] is a semiprimitive c.a.c. ring, we prove that for every essential ideal [math] of [math] containing [math] , [math] is essential in [math] if and only if the set of isolated points of [math] is finite. We apply this result to rings of continuous realvalued functions on a topological space.
</p>projecteuclid.org/euclid.rmjm/1590739302_20200529040131Fri, 29 May 2020 04:01 EDTGround state solutions for the periodic fractional Schrödinger–Poisson systems with critical Sobolev exponenthttps://projecteuclid.org/euclid.rmjm/1590739303<strong>Mingzhu Yu</strong>, <strong>Haibo Chen</strong>, <strong>Weihong Xie</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 719732.</p><p><strong>Abstract:</strong><br/>
We study the fractional Schrödinger–Poisson system with critical Sobolev exponent
(
−
Δ
)
s
u
+
V
(
x
)
u
+
ϕ
u
=
f
(
x
,
u
)
+
K
(
x
)

u

2
s
∗
−
2
u
in
ℝ
3
,
(
−
Δ
)
t
ϕ
=
u
2
in
ℝ
3
,
where [math] denotes the fractional Laplacian of order [math] ; [math] , [math] and [math] are [math] periodic in the [math] variables; [math] is the fractional critical Sobolev exponent in dimension [math] . Under some weaker conditions on [math] , we prove the existence of ground state solutions for such a system via the mountain pass theorem in combination with the concentrationcompactness principle. Our results are new even for [math] .
</p>projecteuclid.org/euclid.rmjm/1590739303_20200529040131Fri, 29 May 2020 04:01 EDTExistence and uniqueness of monotone positive solutions for fractional higherorder BVPshttps://projecteuclid.org/euclid.rmjm/1590739304<strong>Mi Zhou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 733745.</p><p><strong>Abstract:</strong><br/>
We discuss the existence and uniqueness of monotone positive solutions for a class of higherorder nonlinear fractional differential equations infinitepoint boundary value problems (for short, BVPs) on cones. The existence and uniqueness of solutions are obtained via applying the properties of the Green function and a fixed point theorem. Our analysis is based on the operator equation [math] on an ordered Banach space. Finally, a example is given to illustrate our results.
</p>projecteuclid.org/euclid.rmjm/1590739304_20200529040131Fri, 29 May 2020 04:01 EDTEkedahl–Oort strata on the moduli space of curves of genus fourhttps://projecteuclid.org/euclid.rmjm/1590739305<strong>Zijian Zhou</strong>. <p><strong>Source: </strong>Rocky Mountain Journal of Mathematics, Volume 50, Number 2, 747761.</p><p><strong>Abstract:</strong><br/>
We study the induced Ekedahl–Oort stratification on the moduli of curves of genus 4 in positive characteristic by computing the de Rham cohomology of curves. For moduli space of hyperelliptic curves of genus 4 in characteristic 3, we determine the dimension and reducibility of Ekedahl–Oort strata. For moduli space of curves of genus 4 in odd characteristic, we show the existence of certain Ekedahl–Oort strata and discuss the existence of superspecial curves.
</p>projecteuclid.org/euclid.rmjm/1590739305_20200529040131Fri, 29 May 2020 04:01 EDT