A 24-GHz Patch Array with a Power Amplifier/Low-Noise Amplifier MMIC

This paper presents an active patch array designed at 24 GHz. It can be used as a front-end component for a phased array. A series resonant array structure is chosen which is compact and easy excite. With 5 elements, the array proved a 12-dB antenna gain. A power amplifier and a low noise amplifier are designed on a single GaAs chip (PALNA). Bias switch is used in the PALNA, which greatly reduces the switch loss in a transceiver and increases the efficiency. 20-dB small signal gain is achieved in both power amplifier and low noise amplifier. The active patch array is built by the combination of the patch array and PALNA. The measured active gain of this antenna is 35-dB for the PA mode and 31-dB for the LNA mode. This active patch array can obtain an EIRP of 34 dBm with a total radiated power of 22dBm and a maximum PAE of 32%. To check the noise performance, we applied sources at both normal temperature and 77K (liquid nitrogen) and extracted the noise figure (3.5 dB) of the active antenna by the Y factor method. The results proved that the active antenna is working efficiently as both a transmitting and receiving antenna.     

Reciprocally convex functions

We say that f is reciprocally convex if x?f(x) is concave and x?f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented.     

Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law p(ϱ, ϑ) ∼ ϱ ^γ + ϱϑ if γ > 1 and p(ϱ, ϑ) ∼ ϱ ln ^α (1 + ϱ) + ϱϑ if γ = 1, α > 0, depending on the model for the heat flux.     

Picard and weakly Picard operators technique for nonlinear differential equations in Banach spaces

In this paper we study nonlocal Cauchy problems for differential equations in Banach spaces. Using Picard and weakly Picard operators technique and suitable Bielecki norms, some existence, uniqueness and data dependence results are obtained under some mild conditions. As an application, we also discuss a class of impulsive Cauchy problems by adapting the same methods.     

Krull’s theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ₂, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.     

On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.     

Understanding the role of surfactants on the preparation of ZnS nanocrystals

We have synthesized surface modified ZnS nanoparticles of size 2-3 nm using non-ionic surfactant-stabilized reverse emulsions. The non-ionic surfactants in the Span series, i.e. sorbitan monolaurate (Span 20) and sorbitan monooleate (Span 80) of hydrophilic-lipophilic balance (HLB) values of 8.6 and 4.3, respectively, have been used for the stabilization of emulsions. The role of these surfactants in controlling the size and properties of the ZnS nanoparticles has been discussed. The triethylamine (TEA) has been proved to be the effective surface modifying (capping) agent for the preparation of free-standing ZnS nanoparticles. The Span 20 with the higher HLB value of 8.6 has been found to be highly suitable in synthesizing TEA-capped ZnS nanoparticles of smaller size and higher photophysical characteristics compared to that of the Span 80 of lower HLB value of 4.3. A mechanism for the formation of TEA-capped ZnS nanoparticles from the surfactant-stabilized reverse emulsions has been proposed.     

Recent Advances in Asymmetric Catalysis Using p-Block Elements

The development of new methods for enantioselective reactions that generate stereogenic centres within molecules are a cornerstone of organic synthesis. Typically, metal catalysts bearing chiral ligands as well as chiral organocatalysts have been employed for the enantioselective synthesis of organic compounds. In this review, we highlight the recent advances in main group catalysis for enantioselective reactions using the p-block elements (boron, aluminium, phosphorus, bismuth) as a complementary and sustainable approach to generate chiral molecules. Several of these catalysts benefit in terms of high abundance, low toxicity, high selectivity, and excellent reactivity. This minireview summarises the utilisation of chiral p-block element catalysts for asymmetric reactions to generate value-added compounds.