The theorem of consumer surplus and demand elasticity at equilibrium price in a monopolist competition case

In the market of a monopolistically competition the price of a long-run equilibrium, the consumers’ surplus is equal to a half of fixed cost value, and the price elasticity is equal to the ratio of total to fixed costs.consumer surplus; price elasticity

Multiplicities in the length spectrum and growth rate of Salem numbers

We prove that multiplicities in the length spectrum of a non-compact arithmetic hyperbolic orbifold of dimension $n \geqslant 4$ have exponential growth rate $$\langle g(L) \rangle \geqslant c \frac{e^{([n/2] - 1)L}}{L^{1 + \delta_{5, 7}(n) }},$$ extending the analogous result for even dimensions of Belolipetsky, Lal\'in, Murillo and Thompson. Our proof is based on the study of (square-rootable) Salem numbers. As a counterpart, we also prove a refined version of these asymptotic results, adapting the argument of G\"otze and Gusakova for the case of square-rootable Salem numbers, to show that one can not obtain a better estimate on the multiplicities using our approach.Comment: 14 page

Spin-fluctuation theory beyond Gaussian approximation

A characteristic feature of the Gaussian approximation in the functional-integral approach to the spin-fluctuation theory is the jump phase transition to the paramagnetic state. We eliminate the jump and obtain a continuous second-order phase transition by taking into account high-order terms in the expansion of the free energy in powers of the fluctuating exchange field. The third-order term of the free energy renormalizes the mean field, and fourth-order term, responsible for the interaction of the fluctuations, renormalizes the spin susceptibility. The extended theory is applied to the calculation of magnetic properties of Fe-Ni Invar.Comment: 20 pages, 4 figure

Total harmonic distortion of an asymmetric quasi-sinusoidal current

This paper presents the correlation of factors that determine the quality of asymmetric quasi-sinusoidal output current and dynamic losses in the switches of the current generator circuit. The operating mode of the generator was obtained, especially of its power circuit elements, where combination of acceptable output current quality with relatively small dynamic losses in switches and mass-dimensional parameters of the inductor are provided. Achieved results can be used in designing this type of generators

Genome sequencing reveals extraordinary cephalic horns in the Madagascan dung beetle genus Helictopleurus (Coleoptera, Scarabaeinae) : insight from a revision of fungicola species group

In this study, we test and corroborate the phylogenetic position of Heterosyphus within Helictopleurus using mitogenomes and nuclear loci. Our recent samplings revealed that males of the former Heterosyphus sicardi Paulian, 1975 (today under Helictopleurus d'Orbigny, 1915) have extraordinary bilateral clypeal horns which are exclusive within the genus. We provide a taxonomic review of the fungicola species group of Helictopleurus and discuss the systematic position of H. sicardi within the group. The male phenotype of H. sicardi is described and photographs of the body and genitalia of the members of the fungicola group are given, as well as a diagnostic key to species of the group. Helictopleurus fungicola peyrierasi is considered to be a distinct species within the genus (H. peyrierasi stat. rest.). Helictopleurus pluristriatus d'Orbigny, 1915 syn. nov. is established as a junior synonym of H. fungicola (Fairmaire, 1899).Peer reviewe

Design of signal modulator for RF polar transmitter

This paper presents new approach to signal modulation for high efficiency polar transmitter. The new modulator is derived by analyzing complex to polar transforming equations. Once spectral behavior of an envelope and phase signals are known, new architecture offering lower complexity in an analog domain and more flexibility for reconfiguration than a conventional modulator is derived. Concept of the modulator is verified in the course of step-by step simulations with a 5MHz BW input signal at a carrier frequency fC = 2:14GHz. Also, a drain efficiency of a Class E PA driven by the modulator is discussed, and optimal solution for sampling rate is propose

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4+ T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets

On the sequence n! mod pn! \bmod p

We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} + o(1))\sqrt{p}$ distinct residues modulo prime $p$. Moreover, factorials on an interval $\mathcal{I} \subseteq \{0, 1, \dots, p - 1\}$ of length $N > p^{7/8 + \varepsilon}$ produce at least $(1 - o(1))\sqrt{p}$ distinct residues modulo $p$. As a consequence, we obtain a polynomial improvement in the problem of representing a given residue class as a product of seven small factorials.Comment: 9 page