Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of [1], [2]. In particular, we construct the twisted K-theory torus which defines...

Let p be a prime and let a be a positive integer. In this paper we investigate P p a −1 k=0`(h+1)k k+d´/m k modulo a prime p, where d and m are integers with −h < d p a and m ≡ 0 (mod p). We also study congruences involving higher-order Catalan numbers C (h) k = 1 hk+1`(h+1)k k ´ and ¯ C (h) k = h k+1`(h+1)k k ´. Our tools include linear recurrences and the theory of cubic residues. Here are so...

We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That i...

potassium (k) is an element essential for plant growth, playing a significant role in physiological and biochemical processes in plant. the relationship between a soil testing extractant vs. plant nutrient uptake should be a determining parameter in the selection of a soil testing method. the objective of this study was to evaluate different extractants employed for extracting available k in 10...

  We consider the maximal covering location-allocation problem with multiple servers. The objective is to maximize the population covered, subject to constraints on the number of service centers, total number of servers in all centers, and the average waiting time at each center. Each center operates as an M/M/k queuing system with variable number of servers. The total costs of establishing cen...

Fateme Derakhshan-Panah was born in Hamedan (Iran) in 1987. She received her B.S. in Pure Chemistry (2009) and M.S. in Organic Chemistry (2011) from Bu-Ali Sina University, Iran. She is currently working towards her Ph.D. under the supervision of Professor M. A. Zolfigol. Her research interest is organic methodology especially the application of solid acids and ionic liquids in organic synthesis.

1. The main theorems revisited We now state in more detail the main theorems of class field theory. However, we need two more preliminary definitions: Definition 1.1. Given an extension L/K of number fields, and a fractional ideal I of L, we define the fractional ideal N L/K (I) of K as follows: write I = i q ei i , let p i = q i ∩ O K , and let N L/K (I) = i p eifi i. Definition 1.2. Let σ : K...