Maximum compatible classes from compatibility matrices

A fast algorithm for the computation of maximum compatible classes (mcc) among the internal states of an incompletely specified sequential machine is presented in this paper. All the maximum compatible classes are determined by processing compatibility matrices of progressingly diminishing order, whose total number does not exceed (p + m), wherep is the largest cardinality among these classes, andm is the number of such classes. Consequently the algorithm is specially suitable for the state minimization of very large sequential machines as encountered invlsi circuits and systems.     

The Characters of a Sylow p-Subgroup of the Group G2(pn), p≠2, 3

 We compute the irreducible complex characters of a Sylow p-subgroup of the Chevalley group G ₂(q), q=p ⁿ , p≠2, 3 and show that the non linear irreducible characters are induced from linear characters of subgroups of order q ⁵ and q ⁴. Received April 6, 1995     

Conditions for existence of exact solutions of the problem of a fusing wedge

A well-defined condition, determining the values of the aperture angles of a fusing wedge, is presented for exact solutions of the single-phase problem of a fusing wedge that were obtained earlier and are written for these values. The critical orientation of the fusing wedge to the axis of fusion when the written solution degenerates is indicated.Notation , , _n , _n , _n A ₁,A ₂,B auxiliary variables - P _n ,Q _n ,S _n ,T _n polynomials - k, m, n, i natural numbers - , _k angles between the normals to the surfaces forming the fusing wedge - z the axis in a Cartesian coordinate system - U temperature at points of the body infinitely remote from the fusing boundary Voronezh Institute of Technology, Voronezh, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 750–753, June, 1994.     

Computation of the Dimensions of Symmetry Classes of Tensors Associated with the Finite two Dimensional Projective Special Linear Group

The dimensions of the symmetry classes of tensors associated with the projective special linear group of degree 2 over a field with q elements, PSL ₂(q), are found. Of course we will assume PSL ₂(q) as a subgroup of the symmetric group S _{q +1} because this group has a faithful action on the points of the underlying projective space. We also discuss the non-triviality of the symmetry classes of tensors associated with each irreducible character of PSL ₂(q). Received: October 14, 1998; revised version: November 30, 1999     

Isomorphism Classes of Picard Curves over Finite Fields

In this paper we count the number of isomorphism classes of pointed Picard curves, i.e., nonsingular plane curves y³=f(x) of genus 3 with the fixed point at infinity, over finite fields of characteristic different from 3. In the process of doing this we also provide reduced forms of Picard curves that represent the isomorphism classes together with the number of such forms up to isomorphism. In addition to its own theoretical meaning, it has applications to cryptography.     

Superconducting Properties of the Family of Mercurocuprates and Role of Layered Structure

The various phases of the homologous series HgBa₂Ca _n–1Cu _n O_2n+2+ were synthesized earlier using the program-controlled high pressure chamber. We observed that dependence of T _c(a), where a is the in-plane lattice constant (and consequently oxygen content ) have a typical bell-shaped character. T _c versus lattice constant has a similar bell-shaped curve for several values of n, with the maximum T _c value measured for n=3. We have analysed this dependence (and of the formal copper valence) for different members of mercurocuprate family in terms of the phenomenological model of layered superconductors taking into account possible charge redistribution. The experimentally observed nonmonotonic bell-shaped dependence T _c(n) was consistent with our model.     

Ion exchange of intercalation compounds from WOP2O7 and intercalation ofn-alkylamines

Ion exchange of Na _x WOP₂O₇ ·nH₂O (x 1.4) prepared from WOP₂O₇ was attempted, using alkaline and alkaline earth ions. The degree of exchange was observed to be >50% at 90° C except for Mg²⁺. The basal spacing of ion-exchanged materials for the hydrated phase were dependent on the number of water molecules in the interlayer spaces, while those for the dehydrated phase increased with the size of ions in the interlayer spaces. The network of water molecules linked by the hydrogen bond in the interlayer spaces seems to determine the basal spacing. By the ion-exchange reaction,n-alkylammonium ions were intercalated into the interlayer spaces of Na _x WOP₂O₇ ·nH₂O (x 1.4) and Sn _x H _y WOP₂O₇ ·nH₂O (2x +y 0.5). In spite of the difference in the charge density of the host layer, a similar arrangement of alkyl chains in the interlayer spaces resulted, and neutral amines were considered to be intercalated as well as ammonium ions. Direct reaction ofn-alkylamine with WOP₂O₇ produced an intercalation compound without reduction of tungsten. The arrangement of the amines in the interlayer spaces is similar to that supposed to the ion-exchanged derivatives when heated at 140° Cin vacuo.     

Growth of untwinned Bi2Sr2Can?1CunO2n+4+δ thin films on Nd : YAlO3 substrates

Thin film growth of Bi₂Sr₂Ca _n–1Cu _n O_2n+4+ by molecular beam epitaxy is performed on Nd : YAlO₃ (001) substrates. It was revealed that the orthorhombicity of the Nd:YAlO₃ substrate is quite effective to the growth of untwinned Bi₂Sr₂Ca _n–1Cu _n O_2n+4+ thin films. In all phases withn=13, the incommensurate structural modulation lies parallel to the Nd : YAlO₃ [100] direction, and this relation holds even in the case of superlattices. The origin of the epitaxial relation is discussed from the viewpoint of the lattice misfit. The orthorhombicity of the substrate competes with the step edges on a vicinally polished substrate for determining the in-plane growth direction. The rotation of the modulation direction was observed when the off angles are varied.     

Studies of the Vortex Related Phase Transition in YBCO Thin Films with Strong In-Plane Anisotropy

We have studied the vortex-related phase transition in a number of YBCO thin films that have in-plane anisotropy due to the c-axis lying at an angle to the substrate normal. The critical parameters T _t , z, and have been extracted from the scaling of dc I-V measurements made along the two principal transport directions in magnetic fields up to 1 tesla. The dependence of T _t upon the direction of the transport current in some classes of film and the very high z values cast doubt upon the established interpretation based simply upon a vortex liquid–vortex glass phase transition.     

The extraction of ionic conductivities and hopping rates from a.c. conductivity data

Over a wide range of frequencies, the a.c. conductivity of ionic materials shows two regions of frequency-dependent conductivity. These are each characterized by a term K _p ^{1–n n} where K, n are constants, _p is a fundamental frequency identified with the hopping rate and is the measuring frequency. This behaviour is an example of Jonscher's Law of Dielectric Response for ionic conductors. In many cases, the region of low-frequency dispersion approximates to a frequency-independent plateau which may be taken as the d.c. conductivity. In others, a significant low-frequency dispersion is present and cannot be ignored in determining the effective d.c. conductivity. A method for the extraction of d.c. conductivities, hopping rates and for estimating carrier concentration effects is described. Data for three different types of material, single-crystal LiGaO₂, -alumina and Na/Ag -alumina are used to illustrate the method.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Distinctions Between Classes of Superconductors Involve Their Degree of Structural Connectivity

A distinction is made between extreme types, such as highT _c cuprates and soft-metal superconductors concerning the extended, relatively exchange frustration-free covalent ring structures (eight-membered) in the former. Phenomenology indicates for cuprates that bond order (BO) effects within a given number of doped bonds can create real space organization of pairs around O super-exchange centers (trijugate position) within a mobile pair kernel. Indications for this postulated new quantum chemical principle have now been found in related electronic crystal behavior by STM. This situation creates small coherence lengths (∼4 atoms) and unusually high pair numbers. For optimal doping, all holes are converted into pairs and these pairs show trends to geometric checkerboard patterns due to characteristic charge-lattice lock-ins, such as configurations withh _op=0.25 orh _op=0.16. Period of BO and the degree of isolation of the planes determineT _c. Doping curves reflect BO events and are roughly predictable from structural data alone. It is suggested that a variety of related materials with large member rings (e.g. C₆₀) follow the relevant BO phenomenology. By contrast, soft metal superconductors (e.g. Pb) are based on 3D close packed structures with small triangular rings in which exchange interactions are frustrated and small. “Normal” BCS isotope effects suggest the operation of phonons in pair formation over extended coherence lengths (>100 atoms). Very small pair numbers are created through phonons.     

The utility of rat jejunal permeability for biopharmaceutics classification system

Purpose: The biopharmaceutical classification system has been developed to provide a scientific approach for classifying drug compounds based on their dose/solubility ratio and human intestinal permeability. Therefore in this study a new classification is presented, which is based on a correlation between rat and human intestinal permeability values. Methods: In situ technique in rat jejunum was used to determine the effective intestinal permeability of tested drugs. Then three dimensionless parameters—dose number, absorption number, and dissolution number (D_o, A_n, and D_n)—were calculated for each drug. Results: Four classes of drugs were defined, that is, class I, D₀ < 0.5, P_eff(rat) > 5.09 × 10^?5 cm/s; class II, D_o > 1, P_eff(rat) > 5.09 × 10^??5 cm/s; class III, D₀ < 0.5, P_eff(rat) < 4.2 × 10^?5 cm/s; and class IV, D_o > 1, P_eff(rat) < 4.2 × 10^?5 cm/s. A region of borderline drugs (0.5 < D_o < 1, 4.2 × 10^?5 < P_eff(rat) < 5.09 × 10^?5 cm/s) was also defined. Conclusion: According to obtained results and proposed classification for drugs, it is concluded that drugs could be categorized correctly based on dose number and their intestinal permeability values in rat model using single-pass intestinal perfusion technique. This classification enables us to remark defined characteristics for intestinal absorption of all four classes using suitable cutoff points for both dose number and rat effective intestinal permeability values.     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

The Superconducting Bismuth-Based Mixed Oxides

The present paper describes the synthesis, characterization of mixedvalence bismuthates with 3- or 2-dimensional perovskite-like structures and structural criteria that influence superconductivity in these compounds. Single phase samples of Sr_1–x K _x BiO₃ were prepared for the broad range of K-content: 0.25x0.65. For these bismuthates the symmetry of the structure changes from monoclinic to orthorhombic and finally to tetragonal upon increasing the K-content thus resulting in the decrease of the Bi-O distances and reduction of the network distortions. Superconductivity with maximum T _c=12K exists in the narrow range (x0.5–0.6) within the stability field of the tetragonal phase (0.33x0.65), when the 3-dimensional octahedral framework has close to the ideal perovskite structure arrangement. At the same time compositions with close to optimal Bi-valence (x=0.33 and 0.43) do not show any sign of superconductivity, probably, due to structural distortions. The layered type (Ba, K)₃Bi₂O₇ and (Ba, K)₂BiO₄ bismuthates belonging to the A _n+1B _n O_3n+1 homologous series were investigated. Buckling of the (BiO₂) layers in the structure of the n=2 member was revealed. The formation of the n=1 bismuthate was found by Electron Microscopy and X-ray powder diffraction studies. Both types of compounds are considered to be possible candidates for new superconducting materials among bismuthates.     

Stress-strain behaviour of nitrogen bearing austenitic stainless steels in the temperature range 298–473 K

The stress-strain behaviour of three nitrogen-bearing low-nickel austenitic stainless steels has been investigated via a series of tensile tests in the temperature range 298–473 K at an initial strain rate of 1.6×10^–5s^–1. Experimental stress-strain data were analysed employing Rosenbrock's minimization technique in terms of constitutive equations proposed by Hollomon, Ludwik, Voce and Ludwigson. Ludwigson's equation has been found to describe the flow behaviour accurately, followed by Voce's equation. The resultant strain-hardening parameters were analysed in terms of variations in temperature. A linear relationship between ultimate tensile stress and the Ludwigson parameters has been established. The influence of nitrogen on the Ludwigson modelling parameters has also been explained.Nomenclature True stress - _t True strain - _f True fracture strain - Strain rate - T Temperature - K _H, n _H Hollomon parameters - K _L, n _L Ludwik parameters - K _1L, k _2L, n _1L, n _2L Ludwigson parameters - _s, K _V, n _V Voce parameters - _{u relation} Uniform strain computed from a particular relation - _L Transient strain - ₀ Flow stress at zero plastic strain (Ludwik) - _L Transient stress - _y Yield stress - _u Ultimate tensile stress     

Lower bounds for arithmetic networks

We show lower bounds for depth of arithmetic networks over algebraically closed fields, real closed fields and the field of the rationals. The parameters used are either the degree or the number of connected components. These lower bounds allow us to show the inefficiency of arithmetic networks to parallelize several natural problems. For instance, we show a n lower bound for parallel time of the Knapsack problem over the reals and also that the computation of the integer part is not well parallelizable by arithmetic networks. Over the rationals we obtain results of similar order and that the Knapsack has an n lower bound for the parallel time measured by networks. A simply exponential lower bound for the parallel time of quantifier elimination is also shown. Finally, separations among classesP _K andNC _K are available for fieldsK in the above cases.Dedicated to the Memory of Mario RaimondoPartially supported by DGICyT PB 89/0379 and POSSO, ESPRIT-BRA 6846     

A solution to the multivariable matrix factorization problem

Summary Given a para-Hermitian matrix,A(p ₁,p ₂, ...,p _n), whose elements are real, rational functions of the complex variablesp ₁,p ₂, ...,p _n, it is shown thatA (p ₁,p ₂, ...,p _n) can be factorized in the form,A (p ₁,p ₂, ...,p _n)=H ^t (–p ₁, –p ₂, ..., –p _n)H (p₁, p₂, ...,p _n), where the elements of the matrixH (p ₁,p ₂, ...,p _n) are also real rational functions of the specified variables, if and only ifA (j ₁, ...,j _n) is non-negative definite for all real _i, i=1, 2, ...,n. A rather simple computational method for the construction ofH (p ₁,p ₂, ...,p _n) is given, and examples are used to illustrate how, in many cases, the factorization can actually be carried to completion with little labour.     

Bounds on Minimum Distance for Linear Codes over GF(5)

Let [n, k, d; q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). Let d ₅(n, k) be the maximum possible minimum Hamming distance of a linear [n, k, d; 5]-code for given values of n and k. In this paper, forty four new linear codes over GF(5) are constructed and a table of d ₅(n, k) k≤ 8, n≤ 100 is presented.     

Adsorption of hydrogen atom on graphene

The adsorption of atomic hydrogen on graphene monolayer is considered using the model density of states (M model). Analytical expressions for the density of states of H adatom and its occupation number n _a are obtained. The main (local) contribution n _l to the total occupation number n _a is due to a local level of the adatom, which occurs below the edge of the continuous spectrum. A variant of the surface molecule approximation in the case of n _l ≫ n _a − n _l is proposed.