Formula For Number Research Articles

Simulation the effectiveness of heat recovery of the regenerative ventilator using different approaches

Today buildings should be designed for energy efficiency class not less than C. This requires ventilation with heat recovery. On the market, there are different compact heat recovery ventilation units for decentralized ventilation. Regenerative ventilators represent a promising area of effective ventilation with exhaust air heat recovery. They operate cyclically for the inlet and outlet of air. These kinds of ventilators should work in a blocked pair(s) – one for input and one for output in each pair. If not, the effectiveness will decrease. A mathematical model of the ceramic heat regenerator in the regenerative ventilator “Twin Fresh” by Vents has been created to improve the efficiency of its operation. In previous works, on the basis of two different approaches, the operation of the heat regenerator was simulated. The first one uses M. Mikheev’s formula for the Nusselt number. The second one is computational fluid dynamic simulation by SolidWorks Flow Simulation. The efficiency coefficients obtained as a result of the simulation had a significant difference – up to 66.5 %. The aim of the work is to find alternative methods for adequately determining the efficiency of the ventilator. A mathematical simulation was performed using a different formula from “Novyi spravochnik khimika i tekhnologa. Protsessy i aparaty khimicheskikh tekhnologii”. This formula takes into account the Grashof number. Values obtained are significantly different from both previous ones – up to two times. There is no information in the literature about the experimental conditions for determining the Nusselt number, which was used in the simulation. Therefore, we can’t assume, what approach is closer to the conditions of the ceramic regenerator. There is a need to conduct experimental studies to determine the efficiency of the regenerative heat exchanger.

On the enumeration and classification of σ-LCD codes over finite commutative chain rings

Let Re denote a finite commutative chain ring with the maximal ideal 〈u〉 and the nilpotency index e, and let R‾e=Re/〈u〉 be the residue field of Re. Let σ0 be an automorphism of Re, and let σ‾0 be the corresponding automorphism of the residue field R‾e of Re, defined as σ‾0(a+〈u〉)=σ0(a)+〈u〉 for all a+〈u〉∈R‾e. Let σ be an automorphism of Ren corresponding to the automorphism σ0 of Re, defined as σ(v1,v2,…,vn)=(σ0(v1),σ0(v2),…,σ0(vn)) for all (v1,v2,…,vn)∈Ren. In this paper, we obtain explicit enumeration formulae for all σ-LCD codes of an arbitrary length over the chain ring Re when σ‾02 is the identity automorphism of R‾e. With the help of these enumeration formulae and by applying the classification algorithm, we classify all Euclidean LCD codes of lengths 2, 3, 4 and 5 over the chain ring F2[u]/〈u2〉 and of lengths 2, 3 and 4 over the chain ring F3[u]/〈u2〉, and all σ-LCD codes of lengths 2, 3 and 4 over the chain ring F4[u]/〈u2〉, where σ0 is an automorphism of F4[u]/〈u2〉 such that the corresponding automorphism σ‾0 of the residue field F4 has order 2. Besides this, we show that the class of σ-LCD codes over Re is asymptotically good, and that every free linear [n,k,d]-code over Re is equivalent to a σ-LCD [n,k,d]-code over Re when |R‾e|>4. We also explicitly determine all inequivalent σ-LCD [n,1,d]-codes and [n,n−1,d]-codes over Re for 1≤d≤n.

Effects of 25 kHz ultrasound from single and double transducers on thermal and friction characteristics of laminar flows in water or water-based Al2O3 nanofluids

The heat transfer and flow resistance were investigated experimentally in a rectangular duct based on compound techniques of heat transfer enhancement using 25 kHz ultrasound and Al2O3-water nanofluid. The experiment was conducted at flow rates of 0.5–2.0 l/min under constant heat flux and laminar flow conditions. Two ultrasonic transducers were mounted on the top wall of the test section to release the waves from single or double transducers in a downward direction, perpendicular to the mainstream flow. Water and Al2O3(nanoparticle volume fraction (φ) = 0.8–6.1%) nanofluid were utilized as different test fluids. The results showed that the surface temperature increased with the volume fraction of Al2O3, and rapidly reduced after applying the ultrasonic waves. At the same flow rate, the peak augmentation of the local Nusselt number using ultrasound from a single transducer was 1.31 in Al2O3(φ = 6.1%), which increased to 1.58 using double transducers in Al2O3(φ = 1.5%). The flow resistance was increased by adding the Al2O3 nanoparticles, with increased resistance with an increased volume fraction. The friction loss increased up to 3 times for φ = 6.1% compared to the base fluid of water, while it slightly increased approximately 1–2% using ultrasound. These results indicated that using these techniques, the thermal performance tended to increase with a decreased Reynolds number and volume fraction. Finally, predictive formulas for the Nusselt number and friction factor were developed for using single or double ultrasonic transducers in water or Al2O3(φ = 0.8–6.1%) nanofluids under a laminar flow regime.

Dyck Words, Lattice Paths, and Abelian Borders

We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Mathematics, 2014). We extend to any number of distinct abelian borders a result of Rampersad et al. (Developments in Language Theory, 2013) on the exact number of binary words of a given length with no abelian borders. We also generalize these results to partial words.

On the level property of two-dimensional monomial ideals

Let [Formula: see text] be an ideal of the form [Formula: see text] in a polynomial ring [Formula: see text] over a field [Formula: see text], where [Formula: see text] is a prime ideal generated by variables [Formula: see text] for [Formula: see text]. In this paper, we will characterize the level property of [Formula: see text] in the case [Formula: see text] takes a positive value [Formula: see text] or [Formula: see text]. In such a case, we also give an explicit formula for the last Betti number of this ring.

Defect 2 spin blocks of symmetric groups and canonical basis coefficients

This paper addresses the decomposition number problem for spin representations of symmetric groups in odd characteristic. Our main aim is to find a combinatorial formula for decomposition numbers in blocks of defect 2 2 , analogous to Richards’s formula for defect 2 2 blocks of symmetric groups. By developing a suitable analogue of the combinatorics used by Richards, we find a formula for the corresponding “ q q -decomposition numbers”, i.e. the canonical basis coefficients in the level- 1 1 q q -deformed Fock space of type A 2 n ( 2 ) A^{(2)}_{2n} ; a special case of a conjecture of Leclerc and Thibon asserts that these coefficients yield the spin decomposition numbers in characteristic 2 n + 1 2n+1 . Along the way, we prove some general results on q q -decomposition numbers. This paper represents the first substantial progress on canonical bases in type A 2 n ( 2 ) A^{(2)}_{2n} .

Study on the two-component gas apparent permeability model in shale nanopores considering Knudsen number correction

At present, the technology of carbon dioxide flooding shale gas is a hot topic for scholars. The numerical simulation of shale gas driven by carbon dioxide is inseparable from the accurate understanding of gas percolation mechanism and the construction of two-component gas motion equation. During the flooding process, the gas apparent permeability and the Knudsen number both change with time and space. However, this has not been fully discussed in previous studies. In this paper, the percolation mechanisms of two-component gas are discussed. On this basis, the calculation formula of Knudsen number in porous media is modified, and the transport equation of two-component gas is established. According to the derivation of apparent permeability, the two-component gas apparent permeability model is deduced. Then, the correction effect of Knudsen number and the related properties of two-component apparent permeability are analyzed. The results show that: (1) the effect of Knudsen number correction is significant at low pressure. Under high pressure, that is, when the pressure is greater than 10 MPa, the effect can be ignored; (2) the effect of Knudsen number correction is mainly significant in the range of medium pores, which is generally 10 nm–60 nm. And the peak value range decreases with the increase of pressure; (3) for the relative component apparent permeability curve, it has the properties of both relative permeability and apparent permeability. Based on the data in this paper, for the pressure change, it can be concluded that the maximum change rate of methane is 47.79% and that of carbon dioxide is 51.36%. For the change of pore size, it can be concluded that the maximum change rate of methane is 223.45% and that of carbon dioxide is 106.19%. It can be shown that the relative permeability of carbon dioxide is sensitive to pressure and the relative permeability of methane is sensitive to pore size.

Matching in Power Graphs of Finite Groups

The power graph P(G) of a finite group G is the undirected simple graph with vertex set G, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph P_e(G) of G (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of G.

A discrete tick population dynamics model with continuous and seasonal birth breeding

In this paper, we formulate a discrete two-stage model with two types of birth mechanisms, continuous and seasonal. We divide tick population into two subgroups, i.e. immature and mature. We also consider diapause as an important adaptive process for ticks in respond to climate change in both stages. We derive a formula for the inherent net reproductive numbers and explore their stability analysis. When breeding is continuous, there exists a unique globally asymptotically stable positive fixed point provided that the inherent net reproductive number is larger than one; the extinction fixed point is globally asymptotically stable if the inherent net reproductive number is less than one. When breeding is seasonal with 2-periodic birth function, there exists a unique globally asymptotically stable periodic solution provided that the inherent net reproductive number is larger than one, while the population goes to extinction if this value is less than one. For the cases with multi-periodic birth function, we use numerical simulation to compare their complex behaviors.

QUAM-AFM: A Free Database for Molecular Identification by Atomic Force Microscopy.

This paper introduces Quasar Science Resources-Autonomous University of Madrid atomic force microscopy image data set (QUAM-AFM), the largest data set of simulated atomic force microscopy (AFM) images generated from a selection of 685,513 molecules that span the most relevant bonding structures and chemical species in organic chemistry. QUAM-AFM contains, for each molecule, 24 3D image stacks, each consisting of constant-height images simulated for 10 tip-sample distances with a different combination of AFM operational parameters, resulting in a total of 165 million images with a resolution of 256 × 256 pixels. The 3D stacks are especially appropriate to tackle the goal of the chemical identification within AFM experiments by using deep learning techniques. The data provided for each molecule include, besides a set of AFM images, ball-and-stick depictions, IUPAC names, chemical formulas, atomic coordinates, and map of atom heights. In order to simplify the use of the collection as a source of information, we have developed a graphical user interface that allows the search for structures by CID number, IUPAC name, or chemical formula.

Price Index Numbers under Large-Scale Demand Shocks–The Japanese Experience of the COVID-19 Pandemic

Abstract We investigate the prices and quantities of face masks when the 2020 COVID-19 pandemic was particularly serious to understand the impact of demand shocks on the cost of living index (COLI). Using a recently developed index number formula that is exact for the constant elasticity of substitution utility function with variable preferences, we quantified the degree of demand shock caused by the pandemic. Our empirical analysis revealed that shifts in preferences during the pandemic were so large that the COLI with variable tastes became very different from the standard superlative indexes. While the prices of face masks decreased in the Fisher index in May 2020 by 0.76% per week, the COLI increased by 1.92% per week.

“Measuring Inflation under Pandemic Conditions”: A Comment

Abstract Diewert and Fox (2022) examine various implications of the 2020 COVID-19 pandemic for constructing consumer price indexes. The authors state that the pandemic caused major changes in consumption expenditures and shares which makes fixed basket index number formulae inapplicable. They emphasize the need for more frequent surveys of consumer expenditure which will enable compilation of the Fisher index which is considered superior to the traditional Laspeyres or Young indexes. In addition, Diewert and Fox discuss the use of various “new” technologies such as web scraping, scanner data, and information from transactions through credit cards to estimate consumption expenditure.

Approximation numbers of composition operators on weighted besov spaces of analytic functions

AbstractLi et al. [A spectral radius type formula for approximation numbers of composition operators, J. Funct. Anal. 267(12) (2014), 4753-4774] proved a spectral radius type formula for the approximation numbers of composition operators on analytic Hilbert spaces with radial weights and on $H^{p}$ spaces, $p\geq 1$, involving Green capacity. We prove that their formula holds for a wide class of Banach spaces of analytic functions and weights.

Pólya–Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions

We consider coincidence Reidemeister zeta functions for tame endomorphism pairs of nilpotent groups of finite rank, shedding new light on the subject by means of profinite completion techniques.In particular, we provide a closed formula for coincidence Reidemeister numbers for iterations of endomorphism pairs of torsion-free nilpotent groups of finite rank, based on a weak commutativity condition, which derives from simultaneous triangularisability on abelian sections. Furthermore, we present results in support of a Pólya–Carlson dichotomy between rationality and a natural boundary for the analytic behaviour of the zeta functions in question.

An equivariant Hochster's formula for Sn$\mathfrak {S}_n$‐invariant monomial ideals

Let $R=\Bbbk[x_1,\dots,x_n]$ be a polynomial ring over a field $\Bbbk$ and let $I\subset R$ be a monomial ideal preserved by the natural action of the symmetric group $\mathfrak S_n$ on $R$. We give a combinatorial method to determine the $\mathfrak S_n$-module structure of $\mathrm{Tor}_i(I,\Bbbk)$. Our formula shows that $\mathrm{Tor}_i(I,\Bbbk)$ is built from induced representations of tensor products of Specht modules associated to hook partitions, and their multiplicities are determined by topological Betti numbers of certain simplicial complexes. This result can be viewed as an $\mathfrak S_n$-equivariant analogue of Hochster's formula for Betti numbers of monomial ideals. We apply our results to determine extremal Betti numbers of $\mathfrak S_n$-invariant monomial ideals, and in particular recover formulas for their Castelnuovo--Mumford regularity and projective dimension. We also give a concrete recipe for how the Betti numbers change as we increase the number of variables, and in characteristic zero (or $>n$) we compute the $\mathfrak S_n$-invariant part of $\mathrm{Tor}_i(I,\Bbbk)$ in terms of $\mathrm{Tor}$ groups of the unsymmetrization of $I$.

Basic reproduction number for the SIR epidemic in degree correlated networks

The basic reproduction number R0 is an important indicator of the severity for an epidemic outbreak, but it may not be obtained easily for heterogeneous populations especially with biased mixing contacts. Usually, explicit formula for the basic reproduction number in degree correlated networks is difficult to get, thus it is very useful to understand the relationship with their uncorrelated counterparts. It seems that the assortative mixing increases the basic reproduction number of susceptible–infected–recovered (SIR) epidemic, whereas disassortative mixing decreases it, or that assortative mixing enhances the percolation, whereas disassortative mixing weakens it. This result is obtained for degree correlated networks based on a small deviation from the uncorrelated networks, and may not be universal. In this paper, we show rigorously that the result is true for degree correlated networks with arbitrary bimodal degree distribution and for assortative mixing networks with arbitrary degree distribution. However, this may not be always true for general disassortative mixing networks. We also introduce a numerical algorithm to construct an arbitrary joint degree distribution and generate a counterexample of disassortative mixing network that the result fails. Finally, a sufficient condition is given to guarantee that the SIR model in disassortative mixing networks yields smaller R0.

A mathematical model for tilapia lake virus transmission with waning immunity

The goal of this paper is to investigate the influence of the waning immunity on the dynamics of Tilapia Lake Virus (TiLV) transmission in wild and farmed tilapia within freshwater. We formulate a model for which susceptible individuals can contract the disease in two ways: (i) direct mode caused by contact with infected individuals; (ii) indirect mode due to the presence of pathogenic agents in the water. We obtain an age-structured model which combines both age since infection and age since recovery. We derive an explicit formula for the reproductive number and show that the disease-free equilibrium is locally asymptotically stable when, . We discuss on the form of the waning immunity parameter and show numerically that a Hopf bifurcation may occur for suitable immunity parameter values, which means that there is a periodic solution around the endemic equilibrium when, .

Inverse solutions to a vertical plate cooling in air – a comparative study

• The heat transfer coefficient distribution at the vertical surface of a plate cooled in air was determined. • The plate emissivity was simultaneously determined with the convection heat transfer coefficient. • The inverse solution accuracy resulting from the temperature measurement method as well as from the finite element solution to the plate temperature was determined. • It was shown that the boundary condition model which uses the average Nu number did not allow for simultaneous determination of the plate emissivity and the convection heat transfer coefficient. • As a practical part a new formula for the Nusselt number for the vertical plate cooling in air from an initial temperature up to 900°C was developed. Experiments on the vertical plate cooling in air have been performed. The plate made from EN 1.4845 steel was cooled from temperatures of 700°C and 900°C. The plate temperature was recorded at 36 locations. In addition, the cooling chamber temperature and the air temperature were recorded. The selected heat transfer coefficient (HTC) models taken from literature were added to the finite element solver. It has allowed to reveal the models’ accuracy to the measured temperatures. The average temperature error (ATE) varied from 8.2 K to 33.4 K. The best accuracy gave the Churchill and Chu model. The highest ATE gave the Eckert and Jackson formula. It has been shown that the tested models were not sufficient for modeling a vertical plate cooling from high temperatures. Next, an inverse method has been employed to retrieve the convection heat losses simultaneously with the plate emissivity. Two HTC models have been employed in the inverse solution to the convection heat losses at the vertical plate cooled in air. The heat flux at the plate surface was determined as a sum of heat fluxes resulting from natural convection and radiation. The uncertainty tests confirmed a high accuracy of 1.5% of a local HTC model. The decomposition of the total heat flux into the convection and radiation part was possible only in the case of a local HTC model. It has been shown, that during transient cooling of a vertical plate in air the convection heat losses for plate temperature above 200°C differ significantly from that reported in the literature. For practical applications, a new model for calculating the convection heat losses has been proposed. The model involves the temperature excess only as an independent variable. The model can be applied for vertical plates cooling from temperatures reaching up to 900°C.

On condition numbers of the total least squares problem with linear equality constraint

This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Computable expressions and upper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. The results unify the ones for the TLS problem. For TLSE problems with equilibratory input data, numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers-based estimates are much tighter.

Recurrence Relations of Poly-Cauchy Numbers by the r-Stirling Transform

We give some formulas of poly-Cauchy numbers by the r-Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are with Stirling numbers of the first kind. In our case of the classical or poly-Cauchy numbers, the formulas are with Stirling numbers of the second kind. We also discuss annihilation formulas for poly-Cauchy number with negative indices.