1) Define first and second ionization potentials. Why is the second ionization potential greater than the first ionization potential? Discuss three factors affecting IP values of elements? Ans. The minimum energy required to remove the most loosely bound electron from an isolated gaseous atom to convert it into a gaseous ion is called first ionization potential. It is expressed in e.v/atom or k...

A pair of two sequences is called the even periodic (odd periodic) complementary sequence pair if the sum of their even periodic (odd periodic) correlation function is a delta function. The wellknown Golay aperiodic complementary sequence pair (Golay pair) is a special case of even periodic (odd periodic) complementary sequence pair. In this paper, we presented several classes of even periodic ...

Abstract We study random domino tilings of the Aztec diamond with a biased $$2 \times 2$$ 2 × periodic weight function and associate linear flow on an elliptic curve to this model. Our main result is double integral formula for correlation kernel, in which integrand exp...

Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...

Let X be a topological space (an "accessible space," a "1-space," or a " TV-space " in the terminology of Fréchet, Kuratowski, or Alexandroff-Hopf, respectively) and let f(X) = X be a homeomorphism. We use the following terminology, which was suggested by G. A. Hedlund and which is to be carefully distinguished from those terminologies used by Birkhoff, Ayres, Whyburn, and others. A point x of ...

For 0 < a ? 1 / 2 , we define the quadrilateral zeta function Q ( s ) using Hurwitz and periodic functions show that satisfies Riemann's functional equation studied by Hamburger, Heck Knopp. Moreover, prove for any there exist positive constants A T such number of zeros on line segment from 1/2 to + i is greater than whenever ? .

A large number of results in analysis of algorithms contain fluctuations. A typical result might read “The expected number of . . . for large n behaves like log2 n + constant + delta(log2 n), where delta(x) is a periodic function of period one and mean zero.” Examples include various trie parameters, approximate counting, probabilistic counting, radix exchange sort, leader election, skip lists,...

We deal with C(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presente...

We give necessary and sufficient conditions for a divisor in a tube domain to be the divisor of a holomorphic function with almost–periodic modulus. Zero distribution for various classes of holomorphic almost–periodic functions in a strip was studied by many authors (cf. The notion of almost–periodic discrete set appeared in [9] and [17] in connection with these investigations. Its generalizati...