Description Of Multiplication Research Articles

An Insight into Pandemic COVID-19: Structure, Epidemiology and Therapeutics

The coronaviruses are enveloped viruses with a positive-sense ssRNA genome, possess helical symmetry, and belongs to the family Coronaviridae. They cause mild to lethal respiratory tract infections in both mammals and birds. The more pathogenic coronaviruses cause SARS, MERS, and COVID-19. The recent coronavirus outbreak was first discovered in December 2019. Subsequently, the disease has been declared as a pandemic by The World Health Organization (WHO). The virus is named Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the disease is now called COVID-19 [Coronavirus disease 2019]. The primary route of the virus spread between people is through close contact where a healthy person inhales the respiratory droplets from an infected person either by cough or sneezing. More than 2 million confirmed cases are reported globally. The US has the world's largest number of COVID-19 cases followed by European countries. As of April 18, 2020, 2 074 529 confirmed, and 139 378 deaths were reported. Presently, there is no specific drug or vaccine that is approved to treat SARS-CoV-2. The practice of hygienic measures such as frequent hand wash, use of masks, and social distancing would prevent the spread of the disease. This review focuses on a brief description of the viral structure and its multiplication, epidemiology and therapeutics with a special mention on the nanotechnology approach to combat covid-19. This review describes briefly the SARS-CoV-2 viral structure and its multiplication, epidemiology and therapeutics.

Topological Bloch oscillations

Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wavepacket takes to traverse a Brillouin-zone loop. We introduce a new type of Bloch oscillations whose periodicity is an integer ($\mu{>}1$) multiple of the fundamental period. The period multiplier $\mu$ is a topological invariant protected by the space groups of crystals, which include more than just translational symmetries. For example, $\mu$ divides $n$ for crystals with an $n$-fold rotational or screw symmetry; with a reflection, inversion or glide symmetry, $\mu$ equals two. We identify the commonality underlying all period-multiplied oscillations: the multi-band Berry-Zak phases, which encode the holonomy of adiabatic transport of Bloch functions in quasimomentum space, differ pairwise by integer multiples of $2\pi/\mu$. For a class of multi-band subspaces whose projected-position operators commute, period multiplication has a complementary explanation through the real space distribution of Wannier functions. This complementarity follows from a one-to-one correspondence between Berry-Zak phases and the centers of Wannier functions. A Wannier description of period multiplication does not always exist, as we exemplify with band subspaces with either a nonzero Chern number or $\mathbb{Z}_2$ Kane-Mele topological order. To help identify band subspaces with $\mu{>}1$, a general theorem is presented that outputs Zak phases that are symmetry-protected to integer multiples of $2\pi/n$, given the point-group symmetry representation of any gapped band subspace. A cold-atomic experiment that has observed period-multiplied Bloch oscillations is discussed, and directions are provided for future experiments.

Implementation of 14 bits floating point numbers of calculating units for neural network hardware development

An important aspect of modern automation is machine learning. Specifically, neural networks are used for environment analysis and decision making based on available data. This article covers the most frequently performed operations on floating-point numbers in artificial neural networks. Also, a selection of the optimum value of the bit to 14-bit floating-point numbers for implementation on FPGAs was submitted based on the modern architecture of integrated circuits. The description of the floating-point multiplication (multiplier) algorithm was presented. In addition, features of the addition (adder) and subtraction (subtractor) operations were described in the article. Furthermore, operations for such variety of neural networks as a convolution network - mathematical comparison of a floating point (‘less than’ and ‘greater than or equal’) were presented. In conclusion, the comparison with calculating units of Atlera was made.

Cartan Connections on Lie Groupoids and their Integrability

A multiplicatively closed, horizontal $n$-plane field $D$ on a Lie groupoid $G$ over $M$ generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection $D$ is a Cartan connection $\nabla $ on the Lie algebroid of $G$, a notion already studied elsewhere by the author. It is shown that $\nabla $ may be regarded as infinitesimal parallel translation in the groupoid $G$ along $D$. From this follows a proof that $D$ defines a pseudoaction generating a pseudogroup of transformations on $M$ precisely when the curvature of $\nabla $ vanishes. A byproduct of this analysis is a detailed description of multiplication in the groupoid $J^1 G$ of one-jets of bisections of $G$.

Cayley-Dickson algebras and loops

The Cayley-Dickson process is used in connection with square array representations of the Cayley-Dickson algebras. This involves an array operation on square arrays distinct from matrix multiplication. The arrays give a convenient representation of the octonion division algebra and a description of octonion multiplication. The connection between this description of pure octonion multiplication and seven dimensional real space using products related to the commutator and associator of the octonions is extended to the other Cayley-Dickson algebras and the appropriate real vector space.

Electron transport effects in ion induced electron emission

Ion induced electron emission (IIEE) is usually described as a three-step process, i.e. electron excitation by the incident projectile, electron transport (and multiplication) and electron escape through the potential barrier at the surface. In many cases, the first step of the process has been carefully described. The second step of the process, i.e. electron transport and multiplication, has often been treated in a very rough way, a simple decreasing exponential law being sometimes used. It is precisely the aim of the present work to show the importance of a correct description of electron transport and multiplication in a theoretical calculation of IIEE. A short overview of the electron transport models developed for IIEE is given in this work. The so-called “Infinite medium slowing-down model” often used in recent works is evaluated by means of Monte Carlo simulations. In particular, the importance of considering correctly the semi-infinite character of the medium and the boundary condition at the vacuum-medium interface is discussed. Quantities like the electron escape depth are also briefly discussed. This evaluation has been performed in the particular case of protons (25keV<EH+<3MeV, without charge exchange) incident on polycrystalline aluminium targets.

Study of non-equilibrium electron avalanches, application to proportional counters

The process of gas multiplication in uniform and non-uniform electric fields is analyzed on the basis of a numerical solution of the Boltzmann equation, Monte Carlo simulations and experimental gas gain measurements. We give a brief Boltzman equation description of gas multiplication that points out the different behaviour of the ionization coefficient in uniform and non-uniform electric fields. We introduce the concept of quasi equilibrium as an extension of the equilibrium formulation to non-uniform electric fields. Monte Carlo results for the reduced ionization coefficient and reduced gas gain for methane and propane in cylindrical geometry are presented illustrating their simultaneous dependence on the reduced voltage K and the reduced electric field S. Gas gain measurements for a propane-tissue-equivalent gas mixture are presented, which demonstrate this dependence.

On signatures and a subgroup of a central extension to the mapping class group

Atiyah’s work [1] describes the relationship between multiplication in a central extension of the mapping class group of a surface of genus n and the signatures of 4-dimensional manifolds. This work studies a subgroup of the central extension, which comes from the image of a representation of the pure framed braid group on n-strands found in [5], and the signatures of corresponding 4-manifolds via a split exact sequence. We construct a splitting map to prove the sequence is split exact, and we use the splitting to give a topological description of homology classes in 4-dimensional manifolds with non-zero intersection. We conclude with a description of multiplication in the subgroup.

A generalized multiplication correlation model for the description of fast and thermal neutron multiplication in neutron coincidence counting and time interval analysis

In safeguard verification measurements, neutron coincidence and multiplicity counting are commonly applied for the non-destructive assay of large amounts of plutonium. A model to describe the multiplication effects in the sample is needed to obtain unbiased measurement results. Assay of plutonium containers with a neutron coincidence collar lined with a cadmiumsheet generally involves only fast multiplication, since the moderating power of oxygen in plutonium oxides or mixed oxides is too low to generate a thermal neutron population in the sample. In this situation, Böhnel's model for fast, instantaneous multiplication is adequate to describe neutron multiplication and its effects on coincidence counting. When however fresh or spent fuel is assayed under water, thermal multiplication plays an important role. In these measurements conditions Böhnel's model is no longer valid. In this paper a new model, called the generalized multiplication correlation model, is presented. This model allows to describe the combined effect of fast and thermal multiplication in neutron coincidence and multiplicity counting techniques. The generalised multiplication correlation model is based on the identification of different time correlation schemes, which are involved in the detection of correlated neutrons leaking from a multiplying medium. The proposed model allows to describe the singles-, doubles- and triples-rates of fast and thermal neutrons in a medium with fast and thermal multiplication. It is also shown how these count rates can experimentally be obtained from the one- and two-dimensional Rossi-alpha distribution in time interval analysis and how the measurement of these distributions for fast and thermal neutrons allows to obtain the 240 Pu eff -mass.

Avalanche multiplication and breakdown in Ga/sub 0.52/In/sub 0.48/P diodes

The electron and hole photomultiplication characteristics M, and M/sub h/ have been measured in a series of Ga/sub 0.52/In/sub 0.4x/P devices with high field regions ranging from 2.0 /spl mu/m down to the depletion width of a heavily doped p-n junction. The hole ionization coefficient /spl beta/ is found to be slightly higher than the electron ionization coefficient /spl alpha/ at low fields but at high fields they approach one another. /spl alpha/ and /spl beta/ are found to be significantly lower than in GaAs across the entire range of electric fields studied, and the breakdown voltage of Ga/sub 0.52/In/sub 0.48/P is approximately 1.9 times higher than for similar GaAs structures. Contrary to the behavior observed in GaAs, the multiplication characteristics in all except the thinnest structures appear to be relatively unaffected by the dead space, the minimum distance required to gain sufficient energy to initiate impact ionization. In these very thin structures, a local description of multiplication cannot account for the ionization behavior accurately, and therefore, a Monte Carlo (MC) model has been used to reproduce the measured multiplication characteristics and extract the ionization coefficients.

Hydrodynamic description of electron multiplication in the cathode region: elementary beams model

A model of non-local electron multiplication for numerical simulation of gas discharge in the cathode region is suggested. The model is based on a hydrodynamic description of electron 'beams', emitted from the cathode surface and from the plasma in the region of the cathode. Solution of the test problem, i.e. a normal glow discharge in helium under a pressure of 1 Torr, has shown good agreement with a well known Monte Carlo result of Tran et al. (1977). The model presented is 'fast' enough to be used in self-consistent simulations of non-stationary discharges of various types. A numerical simulation was performed with a sudden switch of the 'beam' ionization mechanism to a 'local' one in the steady-state helium glow discharge. It showed that a streamer-like ionization wave was generated. It is suggested that the stationary state of a low-pressure glow discharge is sustained by non-local ionization, whereas the local ionization 'destroys' the steady-state solution.

Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B

The present approach to the mathematical modelling of infectious diseases is based upon the idea that specific immune mechanisms play a leading role in development, course, and outcome of infectious disease. The model describing the reaction of the immune system to infectious agent invasion is constructed on the bases of Burnet's clonal selection theory and the co-recognition principle. The mathematical model of antiviral immune response is formulated by a system of ten non-linear delay-differential equations. The delayed argument terms in the right-hand part are used for the description of lymphocyte division, multiplication and differentiation processes into effector cells. The analysis of clinical and experimental data allows one to construct the generalized picture of the acute form of viral hepatitis B. The concept of the generalized picture includes a quantitative description of dynamics of the principal immunological, virological and clinical characteristics of the disease. Data of immunological experiments in vitro and experiments on animals are used to obtain estimates of permissible values of model parameters. This analysis forms the bases for the solution of the parameter identification problem for the mathematical model of antiviral immune response which will be the topic of the following paper (Marchuk et al., 1991, J. theor. Biol. 15).

Carrier multiplication and avalanche breakdown in self-aligned bipolar transistors

The extraction of the multiplication factor characterizing impact ionization in bipolar transistors is investigated in detail. In particular two d.c. measurement methods, superior in measurement accuracy in comparison with any method published previously, are presented. These methods clearly separate the voltage dependence of the multiplication factor from the voltage dependence of the base Gummel number. The methods presented are shown to yield consistent results and are verified by a comparison with multiplication data derived from breakdown measurements. They allow easy experimental characterization of carrier multiplication effects in bipolar transistors, and provide a valuable tool for the on-chip investigation of inhomogeneities in space charge layers and for the identification of failure mechanisms. The analytical approximation for the multiplication factor due to Miller is found to provide a good description of carrier multiplication in epitaxial base collector junctions in the low-level multiplication regime if BU cbo is substituted by the value BU cbo, m < BU cbo. The methods are applied but not restricted to self-aligned configurations and are of general interest for the precise characterization of impact ionization phenomena in reverse biased pn junctions.

Reduced kinetic description of electron multiplication in gases

A one-dimensional model of electron multiplication in a gas is considered by using a system of moments equations. An approximate expression for the first Townsend ionisation coefficient is derived and found to be in good agreement with the experimental data for a variety of atomic gases.

Ice particle multiplication in cumulus clouds

AbstractIce particle multiplication in shallow supercooled clouds is described by a stochastic process, which depends on collisions between ice particles and supercooled water droplets and drops. The multiplication is a consequence of the riming and drop splintering processes, or possibly just one of them. In the riming process, a large ice particle collects water droplets which eject splinters on freezing. In the drop splintering process, a supercooled drop which collides with a splinter, freezes and may eject splinters. Account is taken of the stronger evidence of significant drop splintering for small supercooled drops by considering those drops with diameters less than 250μm as a separate group. The probability of collision between an ice splinter and a water drop is estimated by considering their fall velocities and assuming a collection efficiency of unity. As a consequence of the small and large water drop division, the ice splinters are also divided; small ice splinters collide with all water drops, but large splinters having fall velocities comparable with those of small water drops collide only with large water drops. The growth of all ice particles by diffusion of water vapour or accretion of water droplets is taken into account, splinters not captured by water drops grow to rimer status after an appropriate time. Rimers are removed from the system at the time they fall through the 0°C isotherm. A rimer may also be formed as a result of the freezing of a large supercooled water drop, following its collision with an ice splinter. As the early production of splinters by such a rimer depends on its initial mass, which equals that of the drop, a distribution of large water drop masses is considered.Generating functions are formulated for the probabilities of particular numbers of the various categories of ice particle existing at a general time t, as a consequence of one initial ice particle. These functions lead to a set of renewal equations for the estimated mean numbers of ice particles at time t. The Laplace transforms of the renewal equations are studied and it is shown that a simple large time analysis provides a valid description of the growth mechanism during most of the cloud lifetime. A small time behaviour marching technique completes the growth description. The large time analysis predicts that A1 exp(p0t) ice particles exist at time t as a consequence of one initial small ice splinter. Values of the growth parameter, p0, are given for many combinations of the physical parameters. An integration of this large time result provides a description of ice particle multiplication initiated by the nucleating particles introduced into a cloud by a constant updraught. A thermal model is also considered and results in growth times near to those obtained for the constant updraught model. These growth times are considerably less than the growth times predicted by earlier workers.The field observations of several workers are all found to be consistent with this analysis. In many situations the most likely explanation of the multiplication involves two processes. These are: splinter production by riming; and the capture of ice splinters by drops, the drops becoming riming agents when they freeze.

Ice particle multiplication in cumulus clouds

Ice particle multiplication in shallow supercooled clouds is described by a stochastic process, which depends on collisions between ice particles and supercooled water droplets and drops. The multiplication is a consequence of the riming and drop splintering processes, or possibly just one of them. In the riming process, a large ice particle collects water droplets which eject splinters on freezing. In the drop splintering process, a supercooled drop which collides with a splinter, freezes and may eject splinters. Account is taken of the stronger evidence of significant drop splintering for small supercooled drops by considering those drops with diameters less than 250μm as a separate group. The probability of collision between an ice splinter and a water drop is estimated by considering their fall velocities and assuming a collection efficiency of unity. As a consequence of the small and large water drop division, the ice splinters are also divided; small ice splinters collide with all water drops, but large splinters having fall velocities comparable with those of small water drops collide only with large water drops. The growth of all ice particles by diffusion of water vapour or accretion of water droplets is taken into account, splinters not captured by water drops grow to rimer status after an appropriate time. Rimers are removed from the system at the time they fall through the 0°C isotherm. A rimer may also be formed as a result of the freezing of a large supercooled water drop, following its collision with an ice splinter. As the early production of splinters by such a rimer depends on its initial mass, which equals that of the drop, a distribution of large water drop masses is considered. Generating functions are formulated for the probabilities of particular numbers of the various categories of ice particle existing at a general time t, as a consequence of one initial ice particle. These functions lead to a set of renewal equations for the estimated mean numbers of ice particles at time t. The Laplace transforms of the renewal equations are studied and it is shown that a simple large time analysis provides a valid description of the growth mechanism during most of the cloud lifetime. A small time behaviour marching technique completes the growth description. The large time analysis predicts that A1 exp(p0t) ice particles exist at time t as a consequence of one initial small ice splinter. Values of the growth parameter, p0, are given for many combinations of the physical parameters. An integration of this large time result provides a description of ice particle multiplication initiated by the nucleating particles introduced into a cloud by a constant updraught. A thermal model is also considered and results in growth times near to those obtained for the constant updraught model. These growth times are considerably less than the growth times predicted by earlier workers. The field observations of several workers are all found to be consistent with this analysis. In many situations the most likely explanation of the multiplication involves two processes. These are: splinter production by riming; and the capture of ice splinters by drops, the drops becoming riming agents when they freeze.

A microprogram metacompiler

We shall call a microprogram metacompiler a system of programs accepting two inputs : a description of an algorithm and a description of a machine on which this algorithm is to be micro-programmed. In our example, the machine is a CASSANDRE description of the Z0001 and the algorithm is an Algol W description of multiplication. The first part of the system analyses the hardware in order to provide a functional network corresponding to the data path, the control hierarchy and a list of incompatibilities. The second part of the system uses this material to produce microprogram schemate. The third part of the system tries to find a time optimized microprogram by a careful allocation of resources.