Constructions for optimal (u×v,{3,4},1,Q)-OOSPCs

Multiple-weight optical orthogonal signature pattern codes (OOSPCs) were introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. In this paper, an upper bound on the maximum code size of a $(u\times v,W,\lambda ,Q)$-OOSPC is obtained. A link between optimal $(u\times v,W,\lambda ,Q)$-OOSPCs and block designs is developed. Several infinite families of optimal $(u\times v,\{3,4\},1,Q)$-OOSPCs are presented by means of semi-cyclic group divisible designs ($(W,Q)$-SCGDDs) and perfect relative difference families.     

Characteristic energy band values and electron attenuation length of a chemical-vapor-deposition diamond (0 0 1)2 × 1 surface

The characteristic energy band values such as the Fermi-level position with respect to valence band top for a boron-doped p-type hydrogen-terminated chemical-vapor-deposition (CVD) diamond (0 0 1)2 × 1 surface and for a clean CVD diamond (0 0 1)2 × 1 surface have been determined by a new method with an accuracy of ±0.02 eV. The electron attenuation length for the clean diamond (0 0 1)2 × 1 surface for the electron kinetic energy of C 1s X-ray photoemission peak by Mg Kα excitation is experimentally determined to be 2.1-2.2 nm. These values are compared and discussed with the previously reported experimental and simulation values.     

Existence of multiple solutions to second-order discrete Neumann boundary value problems

By using the invariant set of descending flow and variational method, we establish the existence of multiple solutions to a class of second-order discrete Neumann boundary value problems. The solutions include sign-changing solutions, positive solutions, and negative solutions. An example is given to illustrate our results.     

Periodic pattern repetition for unbounded solutions to finite difference equations

ABSTRACT

We study a large class of finite difference equations that exhibit a type of periodic pattern repetition in their solutions for certain choices of initial conditions and prove the existence of unbounded solutions.     

Arithmetic structure in sparse difference sets

Using a slight modification of an argument of Croot, Ruzsa and Schoen we establish a quantitative result on the existence of a dilated copy of any given configuration of integer points in sparse difference sets. More precisely, given any configuration {v₁,…,v?} of vectors in Zd, we show that if A⊂d[1,N] with |A|/Nd?CN−1/?, then there necessarily exists r≠0 such that {rv₁,…,rv?}⊆A−A.     

Δ-Strongly summable sequences spaces in 2-normed spaces defined by ideal convergence and an Orlicz function

In this paper, we study certain new difference sequence spaces using ideal convergence and an Orlicz function in 2-normed spaces and we give some relations related to these sequence spaces.     

Quantitation in two-dimensional fluorescence difference gel electrophoresis: effect of protein fixation

Analyzing a large number of unfixed gels in a 2-D fluorescence difference gel electrophoresis (2-DIGE) experiment presents a challenge of avoiding variable protein diffusion within and across the comparison groups. The characteristics of protein detection and quantitation in a 2-D differential in gel fluorescence experiment were compared for gels with and without protein fixation. The current study tests and concludes that when dealing with a large sample size with variable protein diffusion across the 2-D gel over a period of 2-4 days, it is a preferred choice to fix the gel without affecting the protein quantitation.     

The ABC of hyper recursions

Each member of the family of Gauss hypergeometric functions

f_n=₂F₁(a+ε₁n,b+ε₂n;c+ε₃n;z),