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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

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc $ \overline{\mathbb{D}}$ and $ h$ is a nowhere-holomorphic harmonic function on $ \mathbb{D}$ $ \partial{\mathbb{D}}$ $ \mathcal{C}(\overline{\mathbb{D}})$ an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if $ h$, where $ R$ [ABSTRACT FROM AUTHOR]

Let $ G$ $ G\to GL(V)$, where $ V$. Theorem. Assume that either $ char k = 0$ 0$ --> $ char k = p > 0$ $ p \nmid \vert G\vert$ $ \mathbb{P}(V)/G$ $ \mathcal{L}$ $ \mathcal{L}$ $ \mathcal{O}(1)^{\otimes m}$ $ \mathbb{P}(V)$. This partially solves a question raised in the paper of Kannan, Pattanayak and Sardar [Proc. Amer. Math. Soc. 137 (2009), 863-867]. [ABSTRACT FROM AUTHOR]

In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials. [ABSTRACT FROM AUTHOR]

We have shown in an earlier paper that the divisor class group of the centre of a smooth PI algebra with trivial $ K_0$ [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 introduce the notion of $K$-exact $C^{*}$-algebras, in particular $K$-exact groups. We prove that $K$-exactness is stable under direct limits and that coarsely embeddable groups are $K$-exact groups under a technical condition. [ABSTRACT FROM AUTHOR]

In this paper, we prove the nontriviality of the product $h_0b_0tilde {delta }_sin {rm Ext}_A^{s+3,t(s)}(mathbb {Z}_p,mathbb {Z}_p)$ in the classical Adams spectral sequence, where $pgeq 11$, $4leq s

Let $A$ be an asymptotic basis for $mathbb {N}_0$ of some order. By an {em essentiality} of $A$ one means a subset $P$ such that $A backslash P$ is no longer an asymptotic basis of any order and such that $P$ is minimal among all subsets of $A$ with this property. A finite essentiality of $A$ is called an {em essential subset}. In a recent paper, Deschamps and Farhi asked the following two questions: (i) Does every asymptotic basis of $mathbb {N}_0$ possess some essentiality? (ii) Is the number of essential subsets of size at most $k$ of an asymptotic basis of order $h$ (a number they showed to be always finite) bounded by a function of $k$ and $h$ only? We answer the latter question in the affirmative and answer the former in the negative by means of an explicit construction, for every integer $h geq 2$, of an asymptotic basis of order $h$ with no essentialities. [ABSTRACT FROM AUTHOR]

Let $omega (n)$ be the number of distinct prime factors of $n$. For any positive integer $k$ let $n=n_k$ be the smallest positive integer such that $omega (n+1),ldots ,omega (n+k)$ are mutually distinct. In this paper, we give upper and lower bounds for $n_k$. We study the same quantity when $omega (n)$ is replaced by $Omega (n)$, the total number of prime factors of $n$ counted with repetitions. [ABSTRACT FROM AUTHOR]

In this paper, semilocal rings are characterized in different ways; in particular, it is proved that a ring $R$ is semilocal if and only if every descending chain of principal right ideals of $R$, $a_0Rsupseteq a_1Rsupseteq a_2Rsupseteq cdots supseteq a_nRsupseteq cdots text { with }a_{i+1}=a_i-a_ib_ia_i$ eventually terminates. Then modules with semilocal endomorphism rings are characterized by chain conditions. [ABSTRACT FROM AUTHOR]