In this paper p, p1, q are points of E 2 T . The following three propositions are true: (1) Let P be a compact non empty subset of E T . Suppose P is a simple closed curve. Then W-minP ∈ LowerArcP and E-maxP ∈ LowerArcP and W-minP ∈ UpperArcP and E-maxP ∈ UpperArcP. (2) For every compact non empty subset P of E T and for every q such that P is a simple closed curve and LE(q,W-minP, P ) holds q ...

Bu çal??mada, [1] nolu kaynakta ortaya at?lan probleme ili?kin literatürde daha önce yap?lan Feng Qi tipli integral e?itsizlikleri göz önüne al?narak bu tipteki e?itsizliklerinin (p,q)-analoglar? benzer metotlar kullan?larak elde edilmi?tir.

The author considers a class of nonlocal convolution-type ordinary differential equations the form − A ∗ ( g ∘ u ) 1 ′ t = λ f , 0 < $$\begin{equation*} \quad -A{\left({\left(a*(g\,\circ\, u)\right)}(1)\right)}u^{\prime \prime }(t)=\lambda f{\left(t,u(t)\right)}, 1,\nonumber \end{equation*}$$ where $g$ is continuous function satisfying p q $(p,q)$ growth — that is, there exist constants c $c_1$...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...

In this note, we establish $L^p$-bounds for the semigroup $e^{-tq^w(x,D)}$, $t \ge 0$, generated by a quadratic differential operator $q^w(x,D)$ on $\mathbb{R}^n$ that is Weyl quantization of complex-valued form $q$ defined phase space $\mathbb{R}^{2n}$ with non-negative real part $\operatorname{Re} q 0$ and trivial singular space. Specifically, show $e^{-tq^w(x,D)}$ bounded from $L^p(\mathbb{R...

Let E/K be an abelian extension of number fields, with E 6= Q. Let ∆ and n denote the absolute discriminant and degree of E. Let σ denote an element of the Galois group of E/K. We prove the following theorems, assuming the Extended Riemann Hypothesis: (1) There is a degree-1 prime p of K such that ( p E/K ) = σ, satisfying Np ≤ (1 + o(1))(log ∆ + 2n)2. (2) There is a degree-1 prime p of K such ...