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In this paper, we remove the restriction $ z_{0}(x) \geq 0$ $ w_{0}(x) \leq 0$ [ABSTRACT FROM AUTHOR]

In this paper we discuss various refinements and generalizations of a theorem of Sankar Dutta and Paul Roberts. Their theorem gives a criterion for $ d$-dimensional Noetherian Cohen-Macaulay local ring to be a system of parameters, i.e., to have height $ d$ [ABSTRACT FROM AUTHOR]

In this paper we study an operator $ T$ which is $ M$ of $ E$-hypercyclic and use it to answer negatively two questions asked by Madore and Martínez-Avendaño. We also give a sufficient condition for $ T$-hypercyclic for all finite co-dimensional subspaces $ M$. [ABSTRACT FROM AUTHOR]

In this paper, we use the Perron method to prove the existence of viscosity solutions with asymptotic behavior at infinity to Hessian equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove that there exist measures $ d\mu(x)=\gamma(x)dx$ $ \gamma(x)=\gamma_{0}(\vert x\vert)$ $ \gamma_{0}$ $ \mathcal{M}_{\mu}$ does not map $ L^{p}_{\mu}(\mathbb{R}^{n})$ $ L^{p}_{\mu}(\mathbb{R}^{n})$. This result answers an open question of P. Sjögren and F. Soria. [ABSTRACT FROM AUTHOR]

Let $ S=\{(x,y): 0

This paper gives an asymptotic expansion for the solution of the boundary problem with respect to the Laplace-Beltrami operator. We also consider some examples in the domain whose boundary is real ellipsoid, where the boundary problem does not have a $ C^n$ [ABSTRACT FROM AUTHOR]

We study the almost Daugavet property, a generalization of the Daugavet property. We analyze what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is that if $ Z$ such that the quotient space $ X/Z$, then $ Z$ [ABSTRACT FROM AUTHOR]

In this paper we use the divisorial Zariski decomposition to give a more precise version of the algebraic Morse inequalities. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a $#operatorname {P}$-hard problem. On the other hand, we describe an algorithm for this problem which is especially suited for low-dimensional (say dimensions at most $12$) and for highly-symmetric lattices. We use our implementation, which drastically outperforms those of current computer algebra systems, to find the vertices of Voronoi cells and quantizer constants of some prominent lattices. [ABSTRACT FROM AUTHOR]

In this paper we let $G$ be a simple algebraic group and $r$ be a natural number, and consider the codimension in $G$ of the variety of elements $g\in G$ satisfying $g^r=1$. We shall obtain a lower bound for this codimension which is independent of characteristic, and show that it is attained if $G$ is of adjoint type. [ABSTRACT FROM AUTHOR]

The article discusses the problems that arise when derivations on a general Banach algebra is used to classify the commutators in the algebra since it is hard to solve problems on general Banach algebra. A change occurs if an arbitrary Banach algebra is not used but rather algebra L(X) of all bounded linear operators on the Banach space X is used. The underlying structures of the space X will reportedly give enough information about the operators on X to provide a successful solution.

The article proves the existence of minimal models for varieties of log general type II. A canonical ring is described, and establishes that it is finitely generated for every smooth projective variety X. The proof is presented based on ideas and techniques of the minimal model program. It shows that finite generation in dimensional n — 1 implies the existence of flips in dimension n.