A two-valued function f defined on the vertices of a graph G = (V,E), f : V → {−1, 1}, is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. That is, for every v ∈ V, f(N(v)) ≥ 1, where N(v) consists of every vertex adjacent to v. The weight of a total signed dominating function is f(V ) = ∑ f(v), over all vertices v ∈ V . The total ...

In this paper, we give upper bounds on the upper signed domination number of [l, k] graphs, which generalize some results obtained in other papers. Further, good lower bounds are established for the minus ksubdomination number γ−101 ks and signed k-subdomination number γ −11 ks .

This paper proves a finiteness result for families of integral points on a semiabelian variety minus a divisor, generalizing the corresponding result of Faltings for abelian varieties. Combined with the main theorem of the first part of this paper, this gives a finiteness statement for integral points on a closed subvariety of a semiabelian variety, minus a divisor. In addition, the last two se...

The initiation of protein synthesis by Streptococcus faecalis R grown in folate-free culture occurs without N-formylation or N-acylation of methionyl-tRNA(f) (Met). Methionyl-tRNA synthetase and methionyl-tRNA formyltransferase were partially purified from S. faecalis grown under normal culture conditions in the presence of folate (plus-folate); the general properties of the enzymes were determ...

For any non-square integer multiplier \(k\), there is an infinity of triangular numbers multiple other numbers. We analyze the congruence properties indices \(\xi\) Remainders in relations modulo \(k\) come always pairs whose sum equal \((k-1)\), include 0 and only \((k-1)\) if prime, or odd power a even square plus one minus two. If twice number \(n\), set remainders includes also \(n\) \((n^{...

In this paper we construct possible candidates for the minus versions of monopole and instanton knot Floer homologies. For a null-homologous $K\subset Y$ base point $p\in K$, can associate versions, $\underline{\rm KHM}^-(Y,K,p)$ KHI}^-(Y,K,p)$, to triple $(Y,K,p)$. We prove that Seifert surface $K$ induces $\mathbb{Z}$-grading, there is an $U$-map on which degree $-1$. also other basic propert...

We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado’s characterisation a regular remains valid over set positive kth powers provided has at least (1+o(1))k log k thus completely describe which diagonal forms are and not, given sufficiently many In addition, prove supersaturated version theorem for linear restricted e...

OBJECTIVE Our purpose was to describe the surgical procedure, its results, and its complications and to determine whether patients are satisfied with surgical reduction of labia minora in cases of hypertrophy. STUDY DESIGN The records of 163 patients who underwent reduction of the labia minora during a 9-year period were reviewed. The ages of the patients ranged from 12 to 67 years (median, 2...

INTRODUCTION Limited information is available regarding patients' indication for seeking labiaplasty of the labia minora. AIM The aim of this article is to investigate a patient's indications for seeking labiaplasty of the labia minora. METHODS This is a retrospective review of the medical records of all patients undergoing labiaplasty at our clinic over a 27-month period. MAIN OUTCOME ME...