let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

We discuss experimental implications of extending the gauge structure of the Standard Model to include an additional U(1) interaction broken at or near the weak scale. We work with the most general, renormalizable Lagrangian for the SU(2)×U(1)×U(1) sector, with emphasis on the phenomenon of gauge kinetic mixing between the two U(1) gauge fields, and do not restrict ourselves to any of the “cano...

Fix a prime p. For nonnegative integers a, b, and d, we seek a formula for the number of subgroups of order pd in Z/paZ× Z/pbZ. Set Na,b,d = #{H ⊂ Z/pZ× Z/pZ : #H = p}. This is symmetric in a and b (Na,b,d = Nb,a,d), so when it is convenient we can limit attention to the case a ≤ b. Trivially Na,b,d = 0 if d > a + b, so we may assume 0 ≤ d ≤ a + b. For 1 ≤ a ≤ b, and a + b ≥ d, we will see that...

We apply the Dirac bracket quantization to open strings attached to branes in the presence of background antisymmetric field and recover an inherent noncommutativity in the internal coordinates of the brane. 1 E-mail: ardalan, arfaei, [email protected]

In this paper we develop a framework for semi-automated generation of test cases for object oriented programs from formal speci-cations. We use Object-Z as the formal speciication language. We have designed and prototyped a test system called OZTEST. It understands the characteristics of object-oriented speciications including inheritance. OZTEST maps the speciication to a corresponding impleme...