The relationship between solutions of the sinh-Laplace
equation and the determination of various kinds of
surfaces of constant Gaussian curvature, both positive
and negative, will be investigated here. It is shown
that when the metric is given in a particular set
of coordinates, the Gaussian curvature is related to
the sinh-Laplace equation in a direct way. The
fundamental equations of surface theory are found to
yield a type of geometrically based Lax pair for the system.
Given a particular solution of the sinh-Laplace
equation, this Lax can be integrated to determine
the three fundamental vectors related to the surface.
These are also used to determine the coordinate vector 
of the surface. Some specific examples of this procedure 
will be given.

Paul  Bracken

Determination of surfaces in three-dimensional Minkowski and
Euclidean spaces based on solutions of the Sinh-Laplace equation

A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson radical can be written as the sum of a potent element and a nilpotent element. After  discussing some
basic properties of such rings, we investigate their commutativity behavior.

Hazar Abu-Khuzam

Howard E. Bell

Adil Yaqub

A weak periodicity condition for rings

We extend the result in part I, 2003, of
certain inequalities among the generalized power means.

Peng  Gao

On an inequality of Diananda. Part II

The representation theory of infinite wreath product
groups is developed by means of  the relationship
between their group algebras and conjugacy classes
with those of the  infinite symmetric group.
Further, since these groups  are inductive limits of
finite groups, their finite characters can be
classified as limits of normalized irreducible
characters of prelimit finite groups. This
identification is called the &#8220;asymptotic character
formula.&#8221; The <mml:math alttext="$K_0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>K</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>-invariant of the group
<mml:math alttext="$C^\star$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>C</mml:mi><mml:mo>&#8727;</mml:mo></mml:msup></mml:math>-algebra is also determined.

Robert  Boyer

Character theory of infinite wreath products

Consider the minimization problem with a convex separable
objective function over a feasible region defined by linear
equality constraint(s)/linear inequality constraint of the form
“greater than or equal to” and bounds on the variables. A
necessary and sufficient condition and a sufficient condition are
proved for a feasible solution to be an optimal solution to these
two problems, respectively. Iterative algorithms of polynomial
complexity for solving such problems are suggested and convergence
of these algorithms is proved. Some convex functions, important
for problems under consideration, as well as computational results
are presented.

Stefan M. Stefanov

Convex separable minimization problems with a linear
constraint and bounded variables

We study a new family of functions
<mml:math alttext="$Q(X,Y)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, research its properties, and get some fixed point
theorems about this family.

Chi-Ming  Chen

Chi-Lin  Yen

Fixed point theorems for the class <svg style="vertical-align:-2.3205pt" height="15.0875" version="1.1" viewBox="0 0 56.662498 15.0875" width="56.662498" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D444" d="M745 361q0 -134 -83.5 -233t-214.5 -130l16 -11q97 -67 250 -132l-8 -23q-76 3 -131 16q-81 19 -242 125l-20 13q-129 8 -209 91t-80 208q0 160 116 271t289 111q136 0 226.5 -83t90.5 -223zM645 356q0 127 -57.5 201.5t-169.5 74.5q-126 0 -210.5 -104.5t-84.5 -248.5&#xA;q0 -97 46 -166.5t129 -87.5l84 15l29 -19q104 21 169 121.5t65 213.5z" /></g><g transform="matrix(.017,-0,0,-.017,13.118,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,18.999,12.138)"><path id="x1D44B" d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231&#xA;l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" /></g><g transform="matrix(.017,-0,0,-.017,32.462,12.138)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,39.16,12.138)"><path id="x1D44C" d="M667 650l-9 -28q-53 -5 -76 -17t-64 -59q-51 -61 -175 -225q-21 -29 -27 -55l-27 -136q-13 -65 -0.5 -80t83.5 -22l-7 -28h-280l8 28q64 4 81 19t30 83l25 128q6 35 -7 65l-98 231q-17 41 -32.5 52t-68.5 16l8 28h252l-6 -28l-40 -4q-27 -3 -33 -12.5t2 -31.5&#xA;q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" /></g><g transform="matrix(.017,-0,0,-.017,50.702,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g></svg> 

Let <mml:math alttext="$G$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> be a digraph with <mml:math alttext="$n$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> vertices and let <mml:math alttext="$A(G)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> be its
adjacency matrix. A monic polynomial <mml:math alttext="$f(x)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> of degree at most <mml:math alttext="$n$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> is called an annihilating polynomial of <mml:math alttext="$G$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> if <mml:math alttext="$f(A(G)) = 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>. <mml:math alttext="$G$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> is said to be annihilatingly unique if it possesses a unique
annihilating polynomial. Difans and diwheels are two classes of
annihilatingly unique digraphs. In this paper, it is shown that
the complete product of difan and diwheel is annihilatingly unique.

C. S. GAN

The complete product of annihilatingly unique digraphs

We study integral properties of two classes of functions with
negative coefficients defined using differential operators. The
obtained results are sharp and they improve known results.

G. S. S&#259;L&#259;gean

Integral properties of certain classes of analytic functions with
negative coefficients

The purpose of this paper is to introduce and develop a family of
<mml:math alttext="$\mathbb{Z_+}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>ℤ</mml:mi><mml:mo>+</mml:mo></mml:msub></mml:mrow></mml:math>-valued autoregressive processes of order <mml:math alttext="$p$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math> (<mml:math alttext="$\mathrm{INAR}(p)$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>INAR</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>) by
using the generalized multiplication <mml:math alttext="$\odot_F$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mo>⊙</mml:mo><mml:mi>F</mml:mi></mml:msub></mml:math> of van Harn and
Steutel (1982). We obtain various distributional and regression
properties for these models. A number of stationary <mml:math alttext="$\mathrm{INAR}(p)$" id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>INAR</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> processes with specific marginals are presented and are shown to
generalize several existing models.

Emad-Eldin A. A. Aly

Nadjib Bouzar

Stationary solutions for integer-valued autoregressive processes

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<p><em>International Journal of Mathematics and Mathematical Sciences</em> publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.</p>


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International Journal of Mathematics and Mathematical Sciences publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.

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International Journal of Mathematics and Mathematical Sciences

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International Journal of Mathematics and Mathematical Sciences