There are integral trees of diameter 7

A graph G is called integral if all the roots of the characteristic polynomial P(G; x) are integers. In this paper, four integral trees of diameter 7 are given. These integral trees are the first integral trees of diameter 7 which have been found so far.

No star-like trees are Laplacian co-spectral

It is proved in this paper that no two star-like trees are Laplacian co-spectral, and the star-like trees with maximum degree 3 and 4 are determined by their Laplacian spectrum.

A review of Publications of the Faculty of Electrical Engineering Series Mathematics - 1990-2007

This article gives the author index and some statistical data on the whole edition of Publications of the Faculty of Electrical Engineering, Series Mathematics, Volumes 1-18, i.e. from the resumption of the journal in 1990 until 2007.

Some properties of C-reflexive locally convex spaces

In this note, we shall prove that the class of C-reflexive spaces is stable with respect to separated quotient, arbitrary product and sum, which is not the case for the closed subspaces and the dense hyper planes. If the quotient mapping lifts compact disks, then the class of C-reflexive spaces is three-space stable.

Solution of an integral important in the analysis of wire antennas above ground

Analytical solution of an integral important in the analysis of wire antennas above ground is presented in detail. The integral plays an important role in numerical analysis of wire antennas, because for small source-to-field distances it is quasi-singular and thus very demanding for numerical integration. Therefore, its exact analytical solution is preferred.

Ideal membership in signomial rings

The paper presents decidability of ideal membership for finitely generated signomial ideals with rational exponents over computable field K of characteristic 0. We also prove the existence of no-recursive ideals in K[xQ], where xQ = xQ1?.xQn n is a multiplicative copy of the monoid Qn = Q ( ? ( Q.

Inequalities involving inverse circular and inverse hyperbolic functions

Inequalities connecting inverse circular and inverse hyperbolic functions are established. These results are obtained with the aid of an elementary transcendental function which belongs to the family of R-hyper geometric functions discussed in detail in Carlson?s monograph [2].

Critical sets in Latin squares given that they are symmetric

A uniquely completable (UC) set U is a subset of a Latin square L such that L is the only superset of U which is a Latin square. A critical set C of L is a subset of L such that C is uniquely completable and no subset of C has this property. We show that there is a symmetric Latin square with fixed main diagonal entries for each even number, and obtain a uniquely completable partial symmetric Latin square of order 2n for each n and prove that, it is critical set for n = 3, 4, 5 and 6, and make a problem.