Second eigenvalue of the CR Yamabe operator

Let [Formula: see text] be a compact, connected, strictly pseudo-convex CR manifold. In this paper, we give some properties of the CR Yamabe Operator [Formula: see text]. We present an upper bound for the Second CR Yamabe Invariant, when the First CR Yamabe Invariant is negative, and the existence of a minimizer for the Second CR Yamabe Invariant, under some conditions.

Contact Metric Spaces and pseudo-Hermitian Symmetry

We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold M2n+1, n≥2, is locally pseudo-Hermitian symmetric and satisfies ∇ξh=μhϕ, μ∈R, if and only if M is either a Sasakian locally ϕ-symmetric space or a non-Sasakian (k,μ)-space. When n=1, we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry.

Pseudo Convex Framework using Sparse Channel Estimation for Multipath Fading Channels in DS-CDMA Systems

A Direct-Sequence Code-Division Multiple-Access (DS-CDMA) with rake receiver for multiuser system sets up a new dimension in mobile communication system. We propose a pseudo convex framework using an optimum sparse channel estimation technique for DS-CDMA mobile communication systems. Further, the blind channel estimation problem will be examined for rake-based DS-CDMA communication framework with time variant multi-path fading channels This receiver accomplishes an effective assessment of channel according to a maximum convexity criterion, by means of the sparse technique. This estimation method requires a convenient representation of the discrete multipath fading channel based on the sparse theory. In this paper, we have defined a specialized interior-point method for solving large-scale ℓ1 - problem in multiuser detection. Our method can be generalized to handle a variety of extensions such as various channel conditions. A new solution to DS-CDMA based sparse channel estimation is presented in this paper that assures a global optimal solution. Also, it is proven that the said solution can be used as an apparent program that shall enable solutions utilizing interior point techniques involving polynomial time complexity. Through simulation the rationality of the techniques proposed in this paper has been highlighted by results obtained for various modulation schemes and channel parameters. The execution of a pseudo convex framework using sparse channel estimation technique with rake receiver in DS-CDMA framework for multipath fading channels is explored. The overall performance is evaluated in terms of bit error rate (BER) for a range of values of signal to noise ratio (SNR). This framework gives better performance under various modulation schemes using pseudo noise (PN) spreading code. Furthermore, performance of the proposed system is compared with different detectors.

Fuzzy Differential Subordinations Results for λ-pseudo Starlike and λ-pseudo Convex Functions with Respect to Symmetrical Points

In the present work, we establish some fuzzy differential subordination results for λ‑pseudo starlike and λ-pseudo convex functions with respect to symmetrical points in the open unit disk.

Global Connecting Dual Representation of Non-Smooth Multi-Objective Programs using Convex Functions

New classes of vector functions ,namely V-( , , )- pseudo convex and V- ( , , )- quasi convex functions are introduced which are weaker than V-( , , )- convex functions. Sufficient optimality conditions for proper potency and numerous duality theorems for a category of nonsmooth multiobjective programs are obtained under the assumptions of the above said functions.

Strongly pseudo-convex CR space forms

For a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(𝔿n+1) of a hyperbolic space 𝔿n+1 of constant curvature −1.