Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We study generating functions of strict and non-strict order polynomials of series–parallel posets, called order series. These order series are closely related to Ehrhart series and \(h^*\) -polynomials of the associated order polytopes. We explain how they can be understood as algebras over a certain operad of posets. Our main results are based on the fact that the order series of chains form a basis in the space of order series. This allows to reduce the search space of an algorithm that finds for a given power series f(x), if possible, a poset P such that f(x) is the generating function of the order polynomial of P. In terms of Ehrhart theory of order polytopes, the coordinates with respect to this basis describe the number of (internal) simplices in the canonical triangulation of the order polytope of P. Furthermore, we derive a new proof of the reciprocity theorem of Stanley. As an application, we find new identities for binomial coefficients and for finite partitions that allow for empty sets, and we describe properties of the negative hypergeometric distribution. PubDate: 2022-11-17

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We study the existence of weak solutions for the following boundary value problem $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _pu =\displaystyle \frac{\alpha }{ \alpha +\beta }a(x) u ^{\alpha -2}u v ^\beta & \quad {\mathrm{in}} \,\, {\mathcal {S}} {\setminus } {\mathcal {S}}_0, \\ -\Delta _p v =\displaystyle \frac{\beta }{\alpha +\beta }a(x) u ^\alpha v ^{\beta -2} v &\quad {\mathrm{in}} \,\, {\mathcal {S}} {\setminus } {\mathcal {S}}_0, \\ v= u =0 &\quad {\mathrm{in}} \,\,{\mathcal {S}}_0. \end{array}\right. \end{aligned}$$ where \({\mathcal {S}}\) is the Sirpiński gasket on \({\mathbb {R}}^2\) , \({\mathcal {S}}_0\) is its boundary and \(\Delta _p\) is the weak p-Laplacian operator on fractal domain, under some conditions on the function a and the reals \(p, \alpha\) and \(\beta\) . PubDate: 2022-11-17

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Consider the action by change of coordinates in the space of quartic plane curves. We classify the unstable points of this action through a stratification by irreducible, smooth and locally closed subvarieties. Concretely, we show that these varieties parametrize quartic plane curves with specific singularities, we compute their dimensions and closure. In addition, we show that the space of unstable points consists of two irreducible components which are the closure of two of the strata. PubDate: 2022-11-14

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Let K be a number field with the ring of integers R and \(L=K(\alpha )\) . In this work, we give necessary and sufficient conditions on \(a,\; b,\; s,\; n\) so that the irreducible polynomial \(P(X)=X^{p^n}\,+\,a\,X^{p^s}-b\) of R[X] \((n,s\in {\mathbb {N}},\,\, n\, \,>\,\,s)\) of \(\alpha\) is monogenic. We bring forward a family of monogenic extensions over quadratic fields, as result we give their integral bases over \({\mathbb {Q}}\) and absolute discriminants. PubDate: 2022-11-05

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper established the boundedness of singular integral operator for Morrey spaces on local fields built on the rearrangement-invariant Banach function spaces. It gives an extension on the study of the singular integral operators on p-adic Morrey spaces. This studies also cover the generalized Morrey spaces, the Lorentz-Morrey spaces and the Lorentz-Karamata-Morrey spaces on local fields. PubDate: 2022-11-04

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Nikol’skii-type inequalities for entire functions of exponential type on \({\mathbb{R}}^{n}\) for the Lorentz–Zygmund spaces are obtained. Some new limiting cases are examined. Application to Besov–type spaces of logarithmic smoothness is given. PubDate: 2022-11-03

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is considered on a star-shaped graph with nonlocal integral matching condition. This operator is adjoint to the functional-differential operator with frozen argument at the central vertex of the graph. We study the inverse problem that consists in the recovery of the integral condition coefficients from the eigenvalues. We obtain the spectrum characterization, reconstruction algorithms, and prove the uniqueness of the inverse problem solution. PubDate: 2022-11-02

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract For an infinite family of monogenic trinomials \(P(X)=X^3\pm 3rbX-b\in {\mathbb {Z}}[X]\) , arithmetical invariants of the cubic number field \(L={\mathbb {Q}}(\theta )\) , generated by a zero \(\theta\) of \(P(X)\) , and of its Galois closure \(N=L(\sqrt{d_L})\) are determined. The conductor \(f\) of the cyclic cubic relative extension \(N/K\) , where \(K={\mathbb {Q}}(\sqrt{d_L})\) denotes the unique quadratic subfield of \(N\) , is proved to be of the form \(3^eb\) with \(e\in \lbrace 1,2\rbrace\) , which admits statements concerning primitive ambiguous principal ideals, lattice minima, and independent units in \(L\) . The number \(m\) of non-isomorphic cubic fields \(L_1,\ldots ,L_m\) sharing a common discriminant \(d_{L_i}=d_L\) with \(L\) is determined. PubDate: 2022-11-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we define the localization operators associated to the Kontorovich–Lebedev wavelet (KL-wavelet) transform. Next we prove the boundedness and compactness of these operators, we also show that these operators are in Schatten-von Neumann class, we give a trace formula. PubDate: 2022-10-26

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let \(CV_{(0)}(X, A)\) be the algebra of all weighted vector-valued continuous functions with the topology given by the uniform seminorms induced by V. In this paper, we study completeness, m-convexity and locally \(C^{*}\) -property in \(CV_{(0)}(X,A)\) . PubDate: 2022-10-26

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper deals with the time scale model of time-delayed quaternion-valued recurrent neural networks (QVRNNs). Using contraction mapping principle and exponential dichotomy of linear dynamic equations, we derive sufficient conditions for the existence, uniqueness and the global exponential stability of almost periodic solutions to the addressed QVRNNs. Finally, an appropriate example is given to check the feasibility of our obtained results. PubDate: 2022-10-11

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this article, we consider the Cauchy problem of the dissipative quasi-geostrophic equation in critical Fourier–Besov spaces. Using the bilinear-type fixed point theory, we obtain the global well-posedness results and we prove the existence and uniqueness of analytic solutions with small initial data belonging to the critical Fourier–Besov spaces \({\mathscr {F}}B_{p,q}^{1-2\alpha +\frac{2}{p'}} \) . In addition, we show the stability of global solutions. PubDate: 2022-10-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Let \(\alpha \in \mathbb {R}\) and let \(\mathcal {S}\) be a semigroup. The purpose of the present paper is to find the solutions \(f:\mathbb {R} ^{4}\rightarrow \mathcal {S}\) of the parametric (semigroup valued) functional equation $$\begin{aligned}&f(x_{1},y_{1},z_{1},w_{1})f(x_{2},y_{2},z_{2},w_{2}) \\&\quad =f(x_{1}x_{2}+\alpha y_{1}w_{2}+\alpha y_{2}w_{1}+\alpha z_{1}z_{2},x_{1}y_{2}+x_{2}y_{1}+\alpha z_{1}w_{2}+\alpha z_{2}w_{1}, \\&\quad x_{1}z_{2}+x_{2}z_{1}+y_{1}y_{2}+\alpha w_{1}w_{2},x_{1}w_{2}+x_{2}w_{1}+y_{1}z_{2}+y_{2}z_{1}), \end{aligned}$$ which arises from the product in a quartic number field. For \(\alpha \geqslant 0,\) its scalar-valued solutions are determined in [13]. PubDate: 2022-09-30

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We prove that graphs following the model of Barabasi–Albert tree with n vertices are hypoenergetic in the large n limit. PubDate: 2022-09-24

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Bornology is a study of bounded sets, the spaces of such objects, and the naturally associated maps between the spaces of such objects. Previously, the setting for such a study has most often been in the presence of another type of structure such as metrics, topologies, uniformities, and/or, some sort of an algebraic structure with bounded sets being considered only as these were useful in the study of the main objects of concern. Here we carry out a study of bornology with its objects and maps and with these as the focus of the study. We describe the nature of the objects and maps of such things as subspaces, products, quotients, sums, etc., of the resulting category of those spaces. Mathematicians working on research projects centered around various kinds of topology related objects and maps will no doubt find the contents of the present paper very useful and efficient in that these mathematicians will not need to define boundedness related concepts or prove theorems about bounded sets since these items are within this present paper. PubDate: 2022-09-19

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We investigate some geometric properties of Lagrangian surfaces, in the complex Euclidean plane \(\mathbb {C}^2\) , which make a constant angle with respect to a parallel vector field Z. This latter condition means that the angle function, between the tangent planes of the surface and Z, is a constant. The first basic property is that if M is a Lagrangian surface of constant angle with respect to Z, then it also has constant angle with respect to JZ, where J is the standard almost complex structure on \(\mathbb {C}^2\) . In particular, we have that its tangent components \(Z^\top \) and \(J Z^\perp \) are two vector fields on M of constant length. When they are linearly dependent we deduce that M should be part of a Lagrangian cylinder. When they are linearly independent, we have a frame on M. We use this frame to investigate the properties of these surfaces. The Gaussian curvature is not necessarily constant zero as in the case of the Lagrangian cylinder. In particular, if the angle between \(Z^\top \) and \(J Z^\perp \) is constant we prove that M is part of a Lagrangian plane. Finally, we investigate these surfaces with a parametrization and we give a system of two PDE’s in two variables that are the equivalent conditions to be a Lagrangian surface of constant angle. PubDate: 2022-09-16

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper examines the transfer of the Armendariz (resp., weak Armendariz, resp., nil-Armendariz) property to bi-amalgamations. Our results cover previously known results on amalgamations, and provide the construction of various and original examples satisfying the above-mentioned properties. PubDate: 2022-09-10 DOI: 10.1007/s40590-022-00459-y

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper deals with non-self-adjoint second-order Differential Operators with two constant delays \(\tau _i\) , \(i=1,2\) which are less than half the length of the interval. We consider the case when \(\frac{2\pi }{5} \le \tau _i \le \frac{\pi }{2}\) and potentials \(q_k\) are functions from \(L_2 [\tau _k,\pi ]\) , \(k=1,2\) . We study the inverse spectral problem of recovering operators from their spectral characteristics. Four boundary value problems are considered and we prove that delays and potentials are uniquely determined from their spectra. PubDate: 2022-09-05 DOI: 10.1007/s40590-022-00462-3

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In the present note, we provide a partial classification of nearly free conic-line arrangements in the complex plane having nodes, tacnodes, and ordinary triple points. In this setting, our theoretical bound tells us that the degree of such an arrangement is bounded from above by 12. We construct examples of nearly free conic-line arrangements having degree 3, 4, 5, 6, 7, and we prove that in degree 10, 11, and 12, there is no such arrangement. PubDate: 2022-08-30 DOI: 10.1007/s40590-022-00461-4

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Let \(\overline{p}_{-t}(n)\) count the number of t-colored overpartition of n, with t= 5, 7, 11 and 13. We find several infinite families of congruences modulo 16 and 32 for \(\overline{p}_{-t}(n)\) . For example, For each \(\alpha\) , \(\beta\) and \(\gamma \ge 0\) , $$\begin{aligned} \overline{p}_{-11}\left(8\cdot 3^{4\alpha }\cdot 5^{2\beta +2}\cdot 7^{2\gamma }n+t_5\cdot 3^{4\alpha }\cdot 5^{2\beta +1}\cdot 7^{2\gamma }\right)\equiv 0 \pmod {32}, \end{aligned}$$ where \(t_5\in \{7, 23, 31, 39\}.\) PubDate: 2022-08-26 DOI: 10.1007/s40590-022-00464-1