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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]

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 remove the restriction $ z_{0}(x) \geq 0$ $ w_{0}(x) \leq 0$ [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]

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

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

Our aim in this paper is to estimate the weighted Orlicz-Riesz capacity of balls. [ABSTRACT FROM AUTHOR]

In this paper, we describe the flow of 2-surfaces in $ \mathbb{R}^{3}$ $ K^{-\alpha }$ $ \frac{1}{2}<\alpha \leq 1$ $ \alpha \in (0,\frac{1}{2}]$ by Schnürer. [ABSTRACT FROM AUTHOR]

The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module $ B$. Conversely, we show that if such a $ B$, then there exists a closure operation that satisfies the given axioms. [ABSTRACT FROM AUTHOR]

It is well known that the average position or barycenter of generic orbits for the standard tent map is $ 0.5$. In this paper we prove that for any positive integer $ n$ distinct periodic orbits for the standard tent map with the same barycenter. We also provide some patterns of periodic orbits with the same barycenter. [ABSTRACT FROM AUTHOR]

The main result of this paper determines all real meromorphic functions $f$ of finite order in the plane such that $f'$ has finitely many zeros while $f$ and $f^{(k)}$, for some $k geq 2$, have finitely many non-real zeros. [ABSTRACT FROM AUTHOR]

In this paper, we present a number of examples of commutative Banach algebras with various Arens irregularity properties. These examples illustrate in particular that strong Arens irregularity and extreme non-Arens regularity, the two natural concepts of ``maximal'' Arens irregularity for general Banach algebras as introduced by Dales-Lau and Granirer, respectively, are indeed distinct. Thereby, an open question raised by several authors is answered. We also link these two properties to another natural Arens irregularity property. [ABSTRACT FROM AUTHOR]

Hara, Takemura and Yoshida discussed toric ideals arising from two way subtable sum problems and showed that these toric ideals are generated by quadratic binomials if and only if the subtables are either diagonal or triangular. In the present paper, we show that if the subtables are either diagonal or triangular, then their toric ideals possess quadratic Gröbner bases. [ABSTRACT FROM AUTHOR]

In this paper we give a short and simple proof of the remarkable evaluations of multiple zeta values established by D. Bowman and D. M. Bradley. [ABSTRACT FROM AUTHOR]

In this paper, we show that the boundary $partial Sigma (W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{tilde {S}}$ is irreducible, where $W_{tilde {S}}$ is the minimum parabolic subgroup of finite index in $W$. We also provide several applications and remarks. In particular, we show that for a right-angled Coxeter system $(W,S)$, the set ${w^{infty }|win W, o(w)=infty }$ is dense in the boundary $partial Sigma (W,S)$. [ABSTRACT FROM AUTHOR]

In this paper we prove a weighted version of the Khintchine inequalities. [ABSTRACT FROM AUTHOR]