Isomorphic Transformation Research Articles

The novel intermetallic phases TbNiMg and Tb 4+ xNi 2Mg 3− x ( x = 0.2): Synthesis, crystal structure and peculiarities

The novel intermetallic phases TbNiMg and Tb 4+ x Ni 2Mg 3− x ( x = 0.2) were synthesized by heating in a resistance furnace evacuated quartz vials containing Nb-crucibles with element pieces. Scanning electron microscopy coupled with electron microprobe analysis was performed to check microstructure and phases composition. The crystal structures were refined from X-ray single crystal diffraction data. TbNiMg crystallizes in the MoAlB structure type – orthorhombic, Cmcm, oS12, a = 0.36684(4), b = 1.7721(2), c = 0.39855(4) nm, Z = 4, w R 2 = 0.0861, 171 F 2 values, 14 variables; Tb 4+ x Ni 2Mg 3− x crystallizes in the Ru 4Al 3B 2 structure type – tetrahedral, P4 /mmm, tP18, a = 1.08878(2), c = 0.36290(1) nm, Z = 2, w R 2 = 0.0995, 310 F 2 values, 24 variables. Interatomic distances in the studied phases indicate metallic type bonding with strong Tb–Ni interactions. Both structures are two-layers. The crystal chemical peculiarities of these compounds are described and compared applying the intergrowth concept on the base of AlB 2, CsCl and α-Fe simple fragments. Several two-layer structures, including CrB, ZrSi 2, MoAlB and CuGe 4Hf 2, are described as isomorphic group-subgroup transformation derivatives of the α-U structure by means of the Bärnighausen formalism.

Synthesis of γ-MnOOH nanorods and their isomorphous transformation into β-MnO2 and α-Mn2O3 nanorods

γ-MnOOH nanorods with different diameters were synthesized by a simple one-step polymer-assisted hydrothermal method using 50% (wt.%) Mn(NO3)2 solution and PEG-10000 as reagents. The diameters of as-synthesized γ-MnOOH nanorods were well controlled by simply varying the volume of the 50% Mn(NO3)2 solution. The calcination behavior of the as-synthesized γ-MnOOH nanorods was studied. Nanorods of β-MnO2 and α-Mn2O3 were synthesized by calcination at 350 and 600 °C for 1 h respectively.

Lossless abstraction of imperfect information games

Finding an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomorphic abstraction transformation . For a multi-player sequential game of imperfect information with observable actions and an ordered signal space, we prove that any Nash equilibrium in an abstracted smaller game, obtained by one or more applications of the transformation, can be easily converted into a Nash equilibrium in the original game. We present an algorithm, GameShrink , for abstracting the game using our isomorphism exhaustively. Its complexity is õ ( n 2 ), where n is the number of nodes in a structure we call the signal tree. It is no larger than the game tree, and on nontrivial games it is drastically smaller, so GameShrink has time and space complexity sublinear in the size of the game tree. Using GameShrink , we find an equilibrium to a poker game with 3.1 billion nodes—over four orders of magnitude more than in the largest poker game solved previously. To address even larger games, we introduce approximation methods that do not preserve equilibrium, but nevertheless yield ( ex post ) provably close-to-optimal strategies.

Analysis of controllability degree of discrete dynamic system

The following problem is considered. For the initial state of a discrete dynamic system known up to some given accuracy, estimate the accuracy degree of the state the system passes to, having received a given control on the finite time interval. A method for improving the accuracy of determining the final state by isomorphic transformation of the system is proposed.

Amorphization in iron nitride thin films prepared by reactive ion-beam sputtering

Reactive ion-beam sputtering has been used to prepare iron nitride over a wide composition range. It is found that the samples deposited at room temperature exhibit amorphous phase in the composition range from $12\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ nitrogen to $23\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ nitrogen. For samples deposited at liquid nitrogen temperature the system is amorphous up to $35\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ nitrogen. Amorphization can be understood in terms of a frustration in the system due to a competition between $\ensuremath{\alpha}$ and $\ensuremath{\epsilon}$ phases. Kinetic constraints are also found to play a role in the amorphization process. M\"ossbauer measurements suggest that the local order in the amorphous phase consists of a mixture of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Fe}$--like and $\ensuremath{\epsilon}\text{\ensuremath{-}}{\mathrm{Fe}}_{3}\mathrm{N}$--like short-range orders. On the iron rich side the amorphous phase exhibits two-step crystallization, with a primary $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Fe}$ phase precipitating out in the first step. Around $22\phantom{\rule{0.3em}{0ex}}\mathrm{at}.\phantom{\rule{0.2em}{0ex}}%$ nitrogen the system exhibits a single step isomorphous transformation to $\ensuremath{\epsilon}$ phase. Thus, amorphous iron nitride phases exhibit behavior very similar to the conventional transition metal-metalloid amorphous alloys. In the remaining composition range nanocrystalline phases are formed. The amorphous magnetic iron nitride phases are expected to have distinct advantages over their crystalline counterparts in terms of soft magnetic applications.

Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy

Two types of Lie algebras, which are the subalgebras of the Lie algebra A 2 , A 3 respectively, are presented. The resulting loop algebras are following. As their applications, two different integrable couplings of the Yang hierarchy are obtained, called them the double integrable couplings. The Hamiltonian structure of one of them is worked out by a proper linear isomorphic transformation and the quadratic-form identity.

Robust Hurwitz stability of a class of complex polynomials arising from H∞ control theory

AbstractThis paper deals with the Hurwitz stability of a class of complex polynomials arising from H∞ control theory. Using an isomorphic transformation between the complex variables, sufficient and necessary conditions are obtained on the basis of the Sylvester resultant. Moreover, by applying the complete discrimination system for real polynomials, algebraic criteria for the Hurwitz stability can be derived easily. Unlike the known methods with which the stability test involves infinitely many testing steps, our method provides a testing procedure that needs only a finite number of testing steps. As an application, the presented method has been used successfully to study the problem of H∞ Hurwitz stabilization, a problem of simultaneous stabilization of the closed‐loop characteristic polynomial, and a family of complex polynomials of our concern.

The QAP-polytope and the star transformation

Polyhedral Combinatorics has been successfully applied to obtain considerable algorithmic progress towards the solution of many prominent hard combinatorial optimization problems. Until a few years ago, the quadratic assignment problem (QAP) was one of the exceptions. The work of Padberg and Rijal (Location, Scheduling, Design and Integer Programming, Kluwer Academic Publishers, Dordrecht, 1996; Rijal, Ph.D. Thesis, New York University, 1995) has on the one hand yielded some basic facts about the associated quadratic assignment polytope, but has on the other hand shown that investigations even of the very basic questions (like the dimension, the affine hull, and the trivial facets) soon become extremely complicated. In this paper, we propose an isomorphic transformation of the “natural” realization of the quadratic assignment polytope, which simplifies the polyhedral investigations enormously. We demonstrate this by giving short proofs of the basic results on the polytope that indicate that, exploiting the techniques developed in this paper, deeper polyhedral investigations of the QAP now become possible.

Information sharing between heterogeneous uncertain reasoning models in a multi-agent environment: a case study

The issue of information sharing and exchanging is one of the most important issues in the areas of artificial intelligence and knowledge-based systems (KBSs), or even in the broader areas of computer and information technology. This paper deals with a special case of this issue by carrying out a case study of information sharing between two well-known heterogeneous uncertain reasoning models: the certainty factor model and the subjective Bayesian method. More precisely, this paper discovers a family of exactly isomorphic transformations between these two uncertain reasoning models. More interestingly, among isomorphic transformation functions in this family, different ones can handle different degrees to which a domain expert is positive or negative when performing such a transformation task. The direct motivation of the investigation lies in a realistic consideration. In the past, expert systems exploited mainly these two models to deal with uncertainties. In other words, a lot of stand-alone expert systems which use the two uncertain reasoning models are available. If there is a reasonable transformation mechanism between these two uncertain reasoning models, we can use the Internet to couple these pre-existing expert systems together so that the integrated systems are able to exchange and share useful information with each other, thereby improving their performance through cooperation. Also, the issue of transformation between heterogeneous uncertain reasoning models is significant in the research area of multi-agent systems because different agents in a multi-agent system could employ different expert systems with heterogeneous uncertain reasonings for their action selections and the information sharing and exchanging is unavoidable between different agents. In addition, we make clear the relationship between the certainty factor model and probability theory.

Isomorphic transformations of uncertainties for incorporating EMYCIN-style and PROSPECTOR-style systems into a distributed expert system

In the past, expert systems exploited mainly the EMYCIN model and the PROSPECTOR model to deal with uncertainties. In other words, a lot of stand-alone expert systems which use these two models are available. If we can use the Internet to couple them together, their performance will be improved through cooperation. This is because the problem-solving ability of expert systems is greatly improved by the way of cooperation among different expert systems in a distributed expert system. Cooperation between different expert systems with these two heterogeneous uncertain reasoning models is essentially based on the transformations of uncertainties of propositions between these two models. In this paper, we discovered the exactly isomorphic transformations uncertainties between uncertain reasoning models, as used by EMYCIN and PROSPECTOR.

Anomalous plastic flow of cerium near the isomorphic phase transformations under high hydrostatic pressure

Compression tests have been carried out on cerium specimens at room temperature (0.27 T m) under high hydrostatic pressures up to 1.2 GPa. A strong increase of the yield strength was observed for both isomorphic γ and α phases at pressures approaching the γ↔ α isomorphic phase transformations. That increase was in good agreement with the theory of dislocations when the dependence of elastic properties and a lattice parameter of cerium on pressure was applied to calculate the effect of pressure on the yield stress controlled by the edge dislocations. An anomalous strong decrease of the yield stress was observed in both γ and α phases in the vicinity of both γ↔ α phase transformations. That phenomenon was explained as an effect of pressure induced new phase atoms through spreading the cores of edge dislocations. A complete disappearance of work hardening in both γ and α phases was also observed in the wide range of pressures. The influence of hydrostatic pressure on the energy of grain boundaries of both phases was considered to be responsible for that property. The ratio of the grain boundary energy to the Peierls energy is suggested to be a criterion of the work hardening ability of f.c.c. polycrystals.

On Nash's Hidden Assumption

We provide a precise account of those assumptions underlying any solution concept à la Nash for bargaining games, that is, based only on the geometry of the set of utility vectors associated with a set of agreements, plus the utilities in case of disagreement, and disregarding any detail concerning the bargaining process and environment. We show that this basically amounts to assuming what we call invariance to isomorphic transformations in the underlying situation. A precise statement of this basic equivalence requires traveling between Nash's classical setup of sets and points and the world of preferences and alternatives underlying it.Journal of Economic LiteratureClassification Number: C78.

Transport processes close to magnetic axis in quasihelically symmetric stellarators

Transport processes in the region close to the magnetic axis in quasihelically symmetric stellarators are investigated by solving fluid and kinetic equations. It is found that the isomorphic transformation between transport fluxes in quasihelically symmetric stellarators and those in tokamaks is still valid if the dependence of the Fourier amplitude of the magnetic field spectrum on the flux function does not transform accordingly, and if the absolute values are employed in the transformations of orbit size and fraction of trapped particles. It is also found that orbit squeezing effects are less effective in quasihelically symmetric stellarators because the size of the orbit is smaller than that in tokamaks. The bootstrap current density does not vanish on the magnetic axis if dp/dψ remains finite. Here, ψ is the toroidal flux function and p is the plasma pressure. The direction of the bootstrap current density is also opposite to that in tokamaks similar to that in the core region.

Invariance of the figure source equation for the observational transformation

A previous paper presented a method of transforming observed images from figure to 2nd-order differential figure. In this paper, the invariance of the figure source equation for observational transformation is discussed, when the theory is formed with the figure source equation as its core. The redefined observational transformation is constructed using three types of mapping: intensive transformation, blur transformation, and isomorphic transformation. The sets of these transformations form groups, and by making use of algebraic properties, it is possible to categorize the images. Furthermore, it is shown that the commutative law for transformational groups can be derived by analyzing their structure.

On the isomorphous phase transformation in the solid f.c.c. solutions CoH at high pressures

Samples of Co containing 0.2 at.% Fe and consisting of a mixture of approximately equal amounts of the h.c.p. (stable) and f.c.c. (metastable) phases were loaded with hydrogen by a 24 h exposure to a hydrogen atmosphere at 325°C and pressures up to 9 GPa. X-ray diffraction at ambient pressure and 100 K has revealed a steep increase in the lattice parameter of the f.c.c. phase in the samples hydrogenated at 4–6 GPa, corresponding to an increase in the hydrogen content from few atomic per cent to an H/Co atomic ratio of approximately 0.95. This behaviour is interpreted as a supercritical anomaly of an isomorphous phase transformation in the f.c.c. solid solutions. The topology of the T-P phase diagram of the CoH system is discussed in view of these observations.

Solving systems of linear algebraic equations on array processors

We have proposed a modification of the orthogonal Faddeev method [6] for solving various SLAE and also for inversion and pseudoinversion of matrices. The proposed version of the method relies on Householder and Jordan-Gauss methods and its computational complexity is approximately half that of [6]. This method, combined with the matrix-graph method [9] of formalized SPPC structure design, has been applied to synthesize a number of AP architectures that efficiently implement the proposed method. Goal-directed isomorphic and homeomorphic transformations of the LFG of the original algorithm (5) lead to a one-dimensional (linear) AP of fixed size, with minimum hardware and time costs and with minimized input-output channel width.

Reverse If-Conversion

In this paper we present a set of isomorphic control transformations that allow the compiler to apply local scheduling techniques to acyclic subgraphs of the control flow graph. Thus, the code motion complexities of global scheduling are eliminated. This approach relies on a new technique, Reverse If-Conversion (RIC), that transforms scheduled If-Converted code back to the control flow graph representation. This paper presents the predicate internal representation, the algorithms for RIC, and the correctness of RIC. In addition, the scheduling issues are addressed and an application to software pipelining is presented.

Mössbauer effect of amorphous FeCuAg alloy

An amorphous Fe 0.38(Cu 0.5Ag 0.5) 0.62 alloy has been produced by sputtering. Its Mössbauer spectrum at 290 K reveals a broad ferromagnetic sextet with an average hyperfine field H hf ⋍ 235 kOe . After annealing at 420 K, the linewidth of the sextet becomes smaller and h hf ⋍ 270 kOe due to an isomorphic transformation from amorphous to fcc. After annealing at 620 K, the sharp sextet with h hf ⋍ 315 kOe is due to the precipitation of bcc Fe.

On the rebustness of perfect equilibrium in fixed cost sequential bargaining under an isomorphic transformation

Subgame perfect equilibrium realizations in sequential bargaining with fixed cost structures under positive and negative frames are studied. No effects for frame or experience are found. The strong prevalance of PE outcomes is discussed in the context of the fairness constraint found in other studies.

Precise determination of isomorphous and eutectoid transformation temperatures in binary and ternary Zr alloys

Differential thermal analysis (DTA) was used to accurately determine the phase boundary temperatures in the binary and ternary phase diagrams of Zr alloys containing Fe, Cr and O. The effects of heating and cooling rates on the onset temperatures of allotropic, isomorphous and eutectoid phase transformations were investigated both experimentally and theoretically. The phase boundary temperatures were determined by extrapolating the heating or cooling rate to 0 K min−1 using a predictive equation derived in this work. Comparison of theoretical calculation with experimental data showed good agreement.