Scientiae Mathematicae Japonicae

HOMOGENEOUS STATIONARY SOLUTION FOR BCF MODEL DESCRIBING CRYSTAL SURFACE GROWTH

H. Fujimura, A. Yagi

2009 Volume 69 Issue 3 Pages 295-302
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_295

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This paper continues a study on the initial-boundary value problem for a nonlinear parabolic equation of forth order which was presented by Johnson-Orme- Hunt-Graff-Sudijono-Sauder-Orr [9] for describing the process of growth of a crystal surface under molecular beam epitaxy(MBE). In the previous papers [5, 6], we have constructed a dynamical system determined from the model equation and have studied asymptotic behavior of solutions. This paper is then devoted to investigating stability or instability of homogeneous stationary solution. Using the instability dimension, we will make a lower dimension estimate for the attractor of the dynamical system constructed in [5].

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NORM ONE LINEAR PROJECTIONS AND GENERALIZED CONDITIONAL EXPECTATIONS IN BANACH SPACES

TAKASHI HONDA, WATARU TAKAHASHI

2009 Volume 69 Issue 3 Pages 303-313
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_303

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CERTAIN HYPERGEOMETRIC MATRIX FUNCTIONS

K.A.M. Sayyed, M.S. Metwally, M.T. Mohamed

2009 Volume 69 Issue 3 Pages 315-321
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_315

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This paper deals with the study of a new kind of hypergeometric matrix function, say, p-hypergeometric function of the single complex variable z. The integral form and the composition of p-hypergeometric matrix function are investigated.

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A FIXED POINT THEOREM FOR SEMIGROUPS ON METRIC SPACES WITH UNIFORM NORMAL STRUCTURE

Ahmed. H. Soliman

2009 Volume 69 Issue 3 Pages 323-328
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_323

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In this work, we define new generalized uniformly Lipschitzian type conditions for a one-parameter family of selfmappings which is an asymptotically regular semigroup in a complete bounded metric space. Some fixed point results for this semigroup are presented.

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INFORMATION LOSS OF EXTRACTED SERIES IN AR(1) MODEL

Etsuo Kumagai

2009 Volume 69 Issue 3 Pages 329-339
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_329

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Extracting data from the original series in AR(1) model makes the informa tion loss and could not recover the information on the original series from one on the extracted data even if we extracted all data of the original series.

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HÖLDER CONDITIONS IN THE DIVERGENCE THEOREM

WASHEK F. PFEFFER

2009 Volume 69 Issue 3 Pages 341-352
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_341

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In the framework of Lebesgue integration and bounded sets of finite perimeter, we present a straightforward proof of the divergence theorem for bounded vector fields satisfying HÖlder conditions on sets of appropriate Hausdorff measures.

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KIMMERLE CONJECTURE FOR THE HELD AND O’NAN SPORADIC SIMPLE GROUPS

V. BOVDI, A. GRISHKOV, A. KONOVALOV

2009 Volume 69 Issue 3 Pages 353-362
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_353

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Using the Luthar–Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O’Nan sporadic simple groups. We conﬁrm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture.

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FUNCTIONAL DEPENDENCE ON SMALL SETS OF INDICES

W. W. COMFORT, IVAN S. GOTCHEV

2009 Volume 69 Issue 3 Pages 363-377
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_363

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EXTENDED RECIPROCAL ZETA FUNCTION AND AN ALTERNATE FORMULATION OF THE RIEMANN HYPOTHESIS

M. Aslam Chaudhry

2009 Volume 69 Issue 3 Pages 379-385
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_379

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We define an extension of the reciprocal of the zeta function. Some properties of the function are discussed. We prove an alternate criteria for the proof of the Riemann hypothesis and the simplicity of the zeros of the zeta function.

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TALMUDIC BANKRUPTCY PROBLEM: SPECIAL AND GENERAL SOLUTIONS

Isaac Elishakoff, AndrÉ BÉgin-Drolet

2009 Volume 69 Issue 3 Pages 387-403
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_387

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An elementary solution is presented to the special bankruptcy problem described in the Babylonian Talmud. The presented solution pertains to the numerical data presented in the Tractate of Kethuboth 93a. General solution for any combination of data is also given. Solution of the special case appears to be suitable for inclusion in courses on economy, as well as in group study environments.

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ON HIRATA SEPARABLE GALOIS EXTENSIONS

George Szeto, Lianyong Xue

2009 Volume 69 Issue 3 Pages 405-410
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_405

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Let B be a Hirata separable and Galois extension of B^G with Galois group G of order n invertible in B for some integer n, C the center of B, and V_B(B^G) the commutator subring of B^G in B. It is shown that there exist subgroups K and N of G such that K is a normal subgroup of N and one of the following three cases holds: (i) V_B(B^K) is a central Galois algebra over C with Galois group K, (ii) V_B(B^K) is separable C-algebra with an automorphism group induced by and isomorphic with K, and (iii) BK is a central algebra over V_B(B^K) and a Hirata separable Galois extension of B^N with Galois group N/K. More characterizations for a central Galois algebra VB(B^K) are given.

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WEYL TYPE THEOREMS FOR (p, k)-QUASIHYPONORMAL OPERATORS

S. MECHERI, K. TANAHASHI, A. UCHIYAMA

2009 Volume 69 Issue 3 Pages 411-417
Published: 2009
Released on J-STAGE: March 06, 2020

DOIhttps://doi.org/10.32219/isms.69.3_411

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