Certain density theorems applied to the embeddability of iteration semigroups

Aequationes mathematicae - Let A be an additive semigroup of real numbers the additive group generated by which is non-cyclic. Let $$I=(a,b)$$ be an open interval and $$\mathcal {A}=\left\{...     

Analyticity of the Cox–Ingersoll–Ross semigroup

Positivity - We study the analyticity of the Cox–Ingersoll–Ross semigroup generated by $$\begin{aligned} A_r u=\nu ^2 xu''+\gamma u'+\beta x u'-rx u, \end{aligned}$$ in...     

Quadratic functions fulfilling an additional condition along hyperbolas or the unit circle

Aequationes mathematicae - Let $$ S_1 $$ denote the set of all pairs (x, y) of real numbers that fulfill the condition $$ x^2 - y^2 = 1 $$ , and $$ S_2 $$ denote the set of all pairs...     

Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

Semigroup Forum - Let $$f_1(n), \ldots , f_k(n)$$ be polynomial functions of n. For fixed $$n\in \mathbb {N}$$ , let $$S_n\subseteq \mathbb {N}$$ be the numerical semigroup generated by...     

Regularity of Invariant Sets in Variable Internal Damped Wave Equations

Acta Mathematicae Applicatae Sinica, English Series - In this paper we prove that every compact invariant subset $$\mathscr{A}$$ associated with the semigroup Sn,k(t)t≥0 generated by wave...     

Fractional Gaussian estimates and holomorphy of semigroups

Let $$\Omega \subset {\mathbb {R}}^N$$ be an arbitrary open set, $$0<s<1$$ and denote by $$(e^{-t(-\Delta )_{{{\mathbb {R}}}^N}^s})_{t\ge 0}$$ the semigroup on $$L^2({{\mathbb {R}}}^N)$$ generated by the fractional Laplace operator. In the first part of the paper, we show that if T is a self-adjoint semigroup on $$L^2(\Omega )$$ satisfying a fractional Gaussian estimate in the sense that $$|T(t)f|\le Me^{-bt(-\Delta )_{{{\mathbb {R}}}^N}^s}|f|$$, $$0\le t \le 1$$, $$f\in L^2(\Omega )$$, for some constants $$M\ge 1$$ and $$b\ge 0$$, then T defines a bounded holomorphic semigroup of angle $$\frac{\pi }{2}$$ that interpolates on $$L^p(\Omega )$$, $$1\le p<\infty $$. Using a duality argument, we prove that the same result also holds on the space of continuous functions. In the second part, we apply the above results to the realization of fractional order operators with the exterior Dirichlet conditions.     

Identity Bases for Some Non-exact Varieties

Let A₂ be the variety generated by the five-element non-orthodox 0-simple semigroup. This paper presents the identity bases for several subvarieties of A₂ that are not generated by any completely 0-simple or completely simple semigroups. It will be shown that several subvarieties of A₂, including the variety generated by the five-element Brandt semigroup, are hereditarily finitely based.     

Completely regular semigroups in the variety generated by the bicyclic semigroup

We shall show that a completely regular semigroup is in the semigroup variety generated by the bicyclic semigroup if and only if it is an orthogroup whose maximal subgroups are abelian. Therefore the lattice of subvarieties of the variety generated by the bicyclic semigroup contains as a sublattice a countably infinite distributive lattice of semigroup varieties, each of which consists of orthogroups with maximal subgroups that are torsion abelian groups. In particular, every band divides a power of the bicyclic semigroup.Presented by B. M. Schein.     

Evaluation of Gaussian hypergeometric series using Huff’s models of elliptic curves

The Ramanujan Journal - A Huff curve over a field K is an elliptic curve defined by the equation $$ax(y^2-1)=by(x^2-1)$$ where $$a,b\in K$$ are such that $$a^2\ne b^2$$ . In a similar fashion, a...     

Programming under uncertainty: The complete problem

We define the complete problem of a two-stage linear programming under uncertainty, to be:

$$\begin{gathered} Minimize z(x) = E_\xi \{ cx + q^ + y^ + + q^ - y^ - \} \hfill \\ subject to Ax = b \hfill \\ Tx + Iy^ + + Iy^ - = \xi \hfill \\ x \geqq 0,y^ + \geqq 0,y^ - \geqq 0 \hfill \\ \end{gathered} $$     

Indifferentiable hashing to ordinary elliptic $${\mathbb {F}}_{\!q}$$ F q -curves of $$j=0$$ j = 0 with the cost of one exponentiation in $${\mathbb {F}}_{\!q}$$ F q

Designs, Codes and Cryptography - Let $${\mathbb {F}}_{\!q}$$ be a finite field and $$E_b\!: y^2 = x^3 + b$$ be an ordinary (i.e., non-supersingular) elliptic curve (of j-invariant 0) such that...     

On the determination of solutions of simultaneous Pell equations $$x^{2}-(a^{2}-1)y^{2}=y^{2}-pz^{2}=1$$ x 2 - ( a 2 - 1 ) y 2 = y 2 - p z 2 = 1

Periodica Mathematica Hungarica - In this paper, we consider the simultaneous Pell equations 0.1 $$\begin{aligned} x^{2}-(a^{2}-1)y^{2}= &amp; {} 1, \nonumber \\ y^{2}-pz^{2}= &amp; {} 1,...     

On the Diophantine equation $$Cx^{2}+D=2y^{q}$$ C x 2 + D = 2 y q

The Ramanujan Journal - Let C and D denote positive integers such that $$CD&gt;1$$ . In this paper we investigate the solvability of the Diophantine equation $$Cx^{2}+D=2y^{q}$$ , in positive...     

Characterization of distributive semigroup operations on the positive real numbers

Given any cancellative continuous semigroup operation $$\star $$ on the positive real numbers $$\mathbf {R}_+$$ with the ordinary topology, we completely characterize the set $$\mathcal {D}_\star (\mathbf {R}_+)$$ of all cancellative continuous semigroup operations on $$\mathbf {R}_+$$ which are distributed by $$\star $$ in terms of homeomorphism. As a consequence, we show that an arbitrary semigroup operation in $$\mathcal {D}_\star (\mathbf {R}_+)$$ is homeomorphically isomorphic to the ordinary addition $$+$$ on $$\mathbf {R}_+$$.     

On ranks of quadratic twists of a Mordell curve

The Ramanujan Journal - In this article, we consider the quadratic twists of the Mordell curve $$E:y^2=x^3-1$$ . For a square-free integer k, the quadratic twist of E is given by...     

Levi’s Commutator Theorems for Cancellative Semigroups

For every semigroup of finite exponent whose chains of idempotents are uniformly bounded we construct an identity which holds on this semigroup but does not hold on the variety of all idempotent semigroups. This shows that the variety of all idempotent semigroups E is not contained in any finitely generated variety of semigroups. Since E is locally finite and each proper subvariety of E is finitely generated [1, 3, 4], the variety of all idempotent semigroups is a minimal example of an inherently non-finitely generated variety.     

Asymptotics of the system of solutions of a general differential equation with parameter

Ukrainian Mathematical Journal - We consider annth-order differential equation $$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$ with parameter λ ∈...     

BOUNDARY VALUE PROBLEMS OF SINGULARLY PERTURBED INTEGRO－DIFFERENTIAL EQUATIONS

ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＳＩＮＧＵＬＡＲＬＹＰＥＲＴＵＲＢＥＤＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＺＨＯＵＱＩＮＤＥＭＩＡＯＳＨＵＭＥＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＪｉｌｉｎＵｎｉｖｅ...     

Finite basis problem for 2-testable monoids

A monoid S ¹ obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S ¹ is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.     

On the Growth Properties of Solutions for a Generalized Bi-Axially Symmetric Schr\"{o}dinger Equation

In this paper, we have considered the generalized bi-axially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2-V(r)\} \varphi=0,$$ where $\mu,\nu\ge 0$, and $rV(r)$ is an entire function of $r=+(x^2+y^2)^{1/2}$ corresponding to a scattering potential $V(r)$. Growth parameters of entire function solutions in terms of their expansion coefficients, which are analogous to the formulas for order and type occurring in classical function theory, have been obtained. Our results are applicable for the scattering of particles in quantum mechanics.