Every odd perfect number has a prime factor which exceeds

It is proved here that every odd perfect number is divisible by a prime greater than .

     

An algebraic study of BIB designs: A complete solution for v = 6 and k = 3

The set of all distinct blocks of a BIB design is referred to as the support of the design. The family of BIB designs with v = 6 and k = 3 is studied in depth from the view of possible support sizes. Via a linear algebraic technique it is shown that: (i) a BIB design with v = 6 and k = 3 exists if and only if the support size belongs to {10, 14, 16, 17, 18, 19, 20}; (ii) the minimum block size, b, needed to obtain a BIB design with support size $\text{b}{}^1$ is given by:

     

6.

On block Köthe spaces in which the range of every continuous map has a basis     

V. P. Kondakov 《Functional Analysis and Its Applications》1993,27(4):282-284

     

7.

The pascal automorphism has a continuous spectrum     

A.?M.?VershikEmail author 《Functional Analysis and Its Applications》2011,45(3):173-186

In this paper we describe the Pascal automorphism and present a sketch of the proof that its spectrum is continuous on the orthogonal complement of the constants.     

8.

A non-metrizable compact linearly ordered topological space, every subspace of which has a -minimal base     

Wei-Xue Shi 《Proceedings of the American Mathematical Society》1999,127(9):2783-2791

A collection of subsets of a space is minimal if each element of contains a point which is not contained in any other element of . A base of a topological space is -minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space satisfying that is not metrizable and every subspace of has a -minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.

     

9.

The numerical solution of the matrix equationXA+AY=F     

W. D. Hoskins  D. S. Meek  D. J. Walton 《BIT Numerical Mathematics》1977,17(2):184-190

An iterative method for solving the matrix equationXA+AY=F is discussed Algorithms and techniques for accelerating convergence are outlined. The method compares favourably with existing techniques.     

10.

A characterization of a graph which has a 2-factor     

《Applied Mathematics Letters》2000,13(7):9-12

A necessary and sufficient condition of TUTTE-type for a graph to have a 2-factor is presented.     

11.

Rings over which every module has a maximal submodule     

L. A. Koifman 《Mathematical Notes》1970,7(3):215-219

We consider Bass's hypothesis on perfect rings. For commutative rings the question is answered positively, which gives a new characterization of commutative perfect rings. An example is constructed which shows that in general the hypothesis is not true.Translated from Matematicheskie Zametki, Vol. 7, No. 3, pp. 359–367, March, 1970.In conclusion the author wishes to thank L. A. Skornyakov for his interest in this work.     

12.

On rings for which every indecomposable right module has a unique maximal submodule     

Hiroyuki Tachikawa 《Mathematische Zeitschrift》1959,71(1):200-222

     

13.

Analysis of a continuous finite element method for H(\mathrm{curl},\mathrm{div})-elliptic interface problem     

Huoyuan Duan  Ping Lin  Roger C. E. Tan 《Numerische Mathematik》2013,123(4):671-707

In this paper, we develop a continuous finite element method for the curlcurl-grad div vector second-order elliptic problem in a three-dimensional polyhedral domain occupied by discontinuous nonhomogeneous anisotropic materials. In spite of the fact that the curlcurl-grad div interface problem is closely related to the elliptic interface problem of vector Laplace operator type, the continuous finite element discretization of the standard variational problem of the former generally fails to give a correct solution even in the case of homogeneous media whenever the physical domain has reentrant corners and edges. To discretize the curlcurl-grad div interface problem by the continuous finite element method, we apply an element-local $L^2$ projector to the curl operator and a pseudo-local $L^2$ projector to the div operator, where the continuous Lagrange linear element enriched by suitable element and face bubbles may be employed. It is shown that the finite element problem retains the same coercivity property as the continuous problem. An error estimate $\mathcal{O }(h^r)$ in an energy norm is obtained between the analytical solution and the continuous finite element solution, where the analytical solution is in $\prod _{l=1}^L (H^r(\Omega _l))^3$ for some $r\in (1/2,1]$ due to the domain boundary reentrant corners and edges (e.g., nonconvex polyhedron) and due to the interfaces between the different material domains in $\Omega =\bigcup _{l=1}^L \Omega _l$ .     

14.

On rings over which each module has a maximal submodule     

Yasuyuki Hirano 《代数通讯》2013,41(10):3435-3445

     

15.

Distributions supported in a hypersurface and local     

Galia Dafni 《Proceedings of the American Mathematical Society》1998,126(10):2933-2943

We give a necessary condition for a distribution with compact support in a hypersurface to be in the local Hardy space . We apply this condition to prove a result distinguishing two types of Hardy spaces of distributions on a smooth domain .

     

16.

Distributions of positive mass,which maximize a certain generalized energy integral     

Göran Björck 《Arkiv f?r Matematik》1956,3(3):255-269

     

17.

Semigroups for which every S-system has the natural partial order     

C. S. Johnson Jr.  F. R. McMorris 《Semigroup Forum》1974,8(1):51-55

In this note we characterize semigroups S having the property that the relation , defined by x y iff x yS U {y}, partially orders every S-system.Research of second author supported in part by a post-doctoral fellowship in the Biomathematics Program at North Carolina State University under PHS Grant # GM -678 from NIGMS and while on leave from Bowling Green State University.TO ALFRED H. CLIFFORD on his 65th birthday on the 11th of July, 1973     

18.

A rapidly convergent method for the solution of of the matrix equation XA+AY=F     

W.D. Hoskins  D.S. Meek  D.J. Walton 《Journal of Computational and Applied Mathematics》1977,3(3):211-215

An iterative method for solving the matrix equation XA + AY = F is outlined. An algorithm with acceleration parameters is provided.     

19.

Towards F = ma in a General Setting for Lagrangian Mechanics     

Andrew D. Lewis 《Annales Henri Poincare》2000,1(3):569-605

. By using a suitably general definition of a force, one may geometrically cast the Euler-Lagrange equations in a "force balance" form. The key ingredient in such a construction is the Euler-Lagrange 2-force which is a bundle map from the bundle of two-jets into the first contact system. This 2-force can be used as the basis for a geometric presentation of Lagrangian mechanics with external forces and constraints. Also described is the precise correspondence between this 2-force and the Poincaré-Cartan two-form.     

20.

Analysis of a newsvendor which has errors in inventory data records     

Evren Sahin  John Buzacott  Yves Dallery 《European Journal of Operational Research》2008

Although supply chain scholars very often assume the availability of error free data pertaining to the flow of goods that come in and go out of an inventory system as well as the on hand inventory level, some recent investigations show that this may not be true even in facilities where advanced item identification and data capture technologies such as the barcode system are used. This paper proposes a single period model where the inventory data capture process using the barcode system is prone to errors that lead to inaccuracies. In the first part of our work, we derive analytically the optimal policy in presence of errors when both demand and errors are uniformly distributed. In the second part, we examine quantitatively the impact of record inaccuracies on the performance of an inventory system, in terms of additional overage and shortage costs incurred.     

$\text{b}{}^1$	10	14	16	17	18	19	20
$\text{b}$	10	20	20	30	40	30	20

The pascal automorphism has a continuous spectrum

In this paper we describe the Pascal automorphism and present a sketch of the proof that its spectrum is continuous on the orthogonal complement of the constants.     

A non-metrizable compact linearly ordered topological space, every subspace of which has a -minimal base

A collection of subsets of a space is minimal if each element of contains a point which is not contained in any other element of . A base of a topological space is -minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space satisfying that is not metrizable and every subspace of has a -minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.

     

The numerical solution of the matrix equationXA+AY=F

An iterative method for solving the matrix equationXA+AY=F is discussed Algorithms and techniques for accelerating convergence are outlined. The method compares favourably with existing techniques.     

A characterization of a graph which has a 2-factor

A necessary and sufficient condition of TUTTE-type for a graph to have a 2-factor is presented.     

Rings over which every module has a maximal submodule

We consider Bass's hypothesis on perfect rings. For commutative rings the question is answered positively, which gives a new characterization of commutative perfect rings. An example is constructed which shows that in general the hypothesis is not true.Translated from Matematicheskie Zametki, Vol. 7, No. 3, pp. 359–367, March, 1970.In conclusion the author wishes to thank L. A. Skornyakov for his interest in this work.     

Analysis of a continuous finite element method for H(\mathrm{curl},\mathrm{div})-elliptic interface problem

In this paper, we develop a continuous finite element method for the curlcurl-grad div vector second-order elliptic problem in a three-dimensional polyhedral domain occupied by discontinuous nonhomogeneous anisotropic materials. In spite of the fact that the curlcurl-grad div interface problem is closely related to the elliptic interface problem of vector Laplace operator type, the continuous finite element discretization of the standard variational problem of the former generally fails to give a correct solution even in the case of homogeneous media whenever the physical domain has reentrant corners and edges. To discretize the curlcurl-grad div interface problem by the continuous finite element method, we apply an element-local $L^2$ projector to the curl operator and a pseudo-local $L^2$ projector to the div operator, where the continuous Lagrange linear element enriched by suitable element and face bubbles may be employed. It is shown that the finite element problem retains the same coercivity property as the continuous problem. An error estimate $\mathcal{O }(h^r)$ in an energy norm is obtained between the analytical solution and the continuous finite element solution, where the analytical solution is in $\prod _{l=1}^L (H^r(\Omega _l))^3$ for some $r\in (1/2,1]$ due to the domain boundary reentrant corners and edges (e.g., nonconvex polyhedron) and due to the interfaces between the different material domains in $\Omega =\bigcup _{l=1}^L \Omega _l$ .     

Distributions supported in a hypersurface and local

We give a necessary condition for a distribution with compact support in a hypersurface to be in the local Hardy space . We apply this condition to prove a result distinguishing two types of Hardy spaces of distributions on a smooth domain .

     

Semigroups for which every S-system has the natural partial order

In this note we characterize semigroups S having the property that the relation , defined by x y iff x yS U {y}, partially orders every S-system.Research of second author supported in part by a post-doctoral fellowship in the Biomathematics Program at North Carolina State University under PHS Grant # GM -678 from NIGMS and while on leave from Bowling Green State University.TO ALFRED H. CLIFFORD on his 65th birthday on the 11th of July, 1973     

A rapidly convergent method for the solution of of the matrix equation XA+AY=F

An iterative method for solving the matrix equation XA + AY = F is outlined. An algorithm with acceleration parameters is provided.     

Towards F = ma in a General Setting for Lagrangian Mechanics

. By using a suitably general definition of a force, one may geometrically cast the Euler-Lagrange equations in a "force balance" form. The key ingredient in such a construction is the Euler-Lagrange 2-force which is a bundle map from the bundle of two-jets into the first contact system. This 2-force can be used as the basis for a geometric presentation of Lagrangian mechanics with external forces and constraints. Also described is the precise correspondence between this 2-force and the Poincaré-Cartan two-form.     

Analysis of a newsvendor which has errors in inventory data records

Although supply chain scholars very often assume the availability of error free data pertaining to the flow of goods that come in and go out of an inventory system as well as the on hand inventory level, some recent investigations show that this may not be true even in facilities where advanced item identification and data capture technologies such as the barcode system are used. This paper proposes a single period model where the inventory data capture process using the barcode system is prone to errors that lead to inaccuracies. In the first part of our work, we derive analytically the optimal policy in presence of errors when both demand and errors are uniformly distributed. In the second part, we examine quantitatively the impact of record inaccuracies on the performance of an inventory system, in terms of additional overage and shortage costs incurred.