Physical Transformations of Agri-Food Products during Their Convective Drying: Characterization of the Contraction and Isotropicity of Okra

The physical transformations in terms of contraction of okra dimensions during convective drying were examined. During drying, the lateral and longitudinal dimensions of okra decrease over time. The lateral dimensions go from their initial value to around 53%, 65% and 66% of this value after 530 min. The length of the two samples used goes from 8.65 and 9.02 cm to 6.79 and 7.52 cm after 14,300 min, i.e. a variation of 78.50% and 83.37%. All the two directions give variations almost linear depending on the water content. These linear contractions result in a volume contraction of the okra. It considerably decreases in volume during the drying process. The volume goes from 831.32 cm3 to 367.57 cm3 in min, a variation of 44.22%. The isotropic index reveals that okra does not behave the same in the lateral and longitudinal directions. It contracts its diameter more than its length.

Dynamic scaling characteristics of single-phase natural circulation based on different strain transformations

To understand the dynamical system scaling(DSS)analysis theory,the applicability of DSSβ-andω-strain transformation methods for the scaling analysis of complex loops was explored.A simplified model consisting of two loops was established based on the primary and secondary sides of a nuclear reactor,andβ-andω-strain transformation methods were used to ana-lyze the single-phase natural circulation in the primary circuit.For comparison with the traditional method,simplified DSSβ-andω-strain methods were developed based on the standard scaling criterion.The strain parameters in these four methods were modified to form multiple groups of scaled-down cases.The transient process of the natural circulation was simulated using the Relap5 code,and the variation in the dynamic flow characteristics with the strain numbers was obtained using different scaling methods.The results show that both the simplified and standard DSS methods can simulate the dynamic characteristics of natural circulation in the primary circuit.The scaled-down cases in the simplified method exhibit the same geometric scaling and correspond to small core power ratios.By contrast,different scaled-down cases in the standard DSS method correspond to different geometric scaling criteria and require more power.The dynamic process of natural circula-tion can be simulated more accurately using the standard DSS method.

Literature Review of Phase Transformations and Cavitation Erosion of Duplex Stainless Steels

Phase transformation is one of the factors that would significantly influence the ability to resist cavitation erosion of stainless steels. Due to the specific properties of duplex stainless steel, the heat treatment would bring about significant phase transformations. In this paper, we have examined the previous studies on the phase transition of stainless steel, including the literature on the classification of stainless steel, spinodal decomposition, sigma phase transformation, and cavitation erosion of double stainless steel. Through these literature investigations, the destruction of cavitation erosion on duplex stainless steel can be clearly known, and the causes of failure of duplex stainless steel in seawater can be clarified, thus providing a theoretical basis for subsequent scientific research. And the review is about to help assess the possibility of using bulk heat treatment to improve the cavitation erosion (CE) behaviour of the duplex stainless steel 7MoPLUS.

Nonstandard Unitary Transformations of Quantum States

In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.

In the Atmosphere and Oceanic Fluids:Scaling Transformations,Bilinear Forms,Bäcklund Transformations and Solitons for A Generalized Variable-Coefficient Korteweg-de Vries-Modified Korteweg-de Vries Equation

The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere,oceanic fluids and plasmas.With symbolic computation,beginning with a presumption,we work out certain scaling transformations,bilinear forms through the binary Bell polynomials and our scaling transformations,N solitons(with N being a positive integer)via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons.In addition,Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out.Respective dependences and constraints on the variable/constant coefficients are discussed,while those coefficients correspond to the quadratic-nonlinear,cubic-nonlinear,dispersive,dissipative and line-damping effects in the atmosphere,oceanic fluids and plasmas.

Helmholtz Theorems, Gauge Transformations, General Covariance and the Empirical Meaning of Gauge Conditions

It is well known that the use of Helmholtz decomposition theorem for static vector fields , when applied to the time dependent vector fields , which represent the electromagnetic field, allows us to obtain instantaneous-like solutions all along . For this reason, some people thought (see e.g. [1] and references therein) that the Helmholtz theorem cannot be applied to time dependent vector fields and some modification is wanted in order to get the retarded solutions. However, the use of the Helmholtz theorem for static vector fields is correct even for time dependent vector fields (see, e.g. [2]), so a relation between the solutions was required, in such a way that a retarded solution can be transformed in an instantaneous one, and conversely. On this paper we want to suggest, following most of the time the mathematical formalism of Woodside in [3], that: 1) there are many Helmholtz decompositions, all equally consistent, 2) each one is naturally related to a space-time structure, 3) when we use the Helmholtz decomposition for the electromagnetic potentials it is equivalent to a gauge transformation, 4) there is a natural methodological criterion for choosing the gauge according to the structure postulated for a global space-time, 5) the Helmholtz decomposition is the manifestation at the level of the fields that a gauge is involved. So, when we relate the retarded solution to the instantaneous one what we do is to change the gauge and the space-time. And, if the Helmholtz decompositions are related to a space-time structure, and are equivalent to gauge transformations, each gauge transformation is natural for a specific space-time. In this way, a Helmholtz decomposition for Euclidean space is equivalent to the Coulomb gauge and a Helmholtz decomposition for the Minkowski space is equivalent to the Lorenz gauge. This leads us to consider that the theories defined by different gauges may be mathematically equivalent, because they can be related by means of a gauge transformation, but they are not empirically equivalent, because they have quite different observational consequences due to the different space-time structure involved.

SYMMETRIES， BāCKLUND TRANSFORMATIONS AND BOUNDARY－INITIAL VALUE PROBLEMS FOR NONLINEAR CHROMATOGRAPH

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Peri-Urban Transformations in Agricultural Landscapes of Perugia, Italy

Urban fringes represent very complex landscapes because of their proximity and mutual dependency with cities and rural areas. These landscapes may be considered as transition entities characterized by fuzzy boundaries. An uncontrolled development of urban sprawl and land use changes in these areas may deter- mine negative impacts on all natural, economic and social components. Thus, urban fringes assume a key-role in modern landscape analysis, planning and management. Landscape analysis of these interfaces, as this study shows, can be effectively supported by GIS spatial modelling. The Settlement Density Index (SDI), developed through GIS spatial analysis techniques, expresses punctually the territorial gradients generated by the presence of settlements and allows the identification of the urban fringes in the two periods under invest-tigation. These areas are then characterized and analyzed quantitatively using detailed land use data. The comparison of the diachronic information highlights the transformations of peri-urban landscapes that appear mainly related to the modifications of spatial configuration of urban areas and to the changes of agricultural systems.

Canonical Transformations, Quantization, Mutually Unbiased and Other Complete Bases

Using ideas based on supersymmetric quantum mechanics, we design canonical transformations of the usual position and momentum to create generalized “Cartesian-like” positions, W, and momenta, Pw , with unit Poisson brackets. These are quantized by the usual replacement of the classical , x Px by quantum operators, leading to an infinite family of potential “operator observables”. However, all but one of the resulting operators are not Hermitian (formally self-adjoint) in the original position representation. Using either the chain rule or Dirac quantization, we show that the resulting operators are “quasi-Hermitian” relative to the x-representation and that all are Hermitian in the W-representation. Depending on how one treats the Jacobian of the canonical transformation in the expression for the classical momentum, Pw , quantization yields a) continuous mutually unbiased bases (MUB), b) orthogonal bases (with Dirac delta normalization), c) biorthogonal bases (with Dirac delta normalization), d) new W-harmonic oscillators yielding standard orthonormal bases (as functions of W) and associated coherent states and Wigner distributions. The MUB lead to W-generalized Fourier transform kernels whose eigenvectors are the W-harmonic oscillator eigenstates, with the spectrum (±1,±i) , as well as “W-linear chirps”. As expected, W,?Pw satisfy the uncertainty product relation: ΔWΔPw ≥1/2 , h=1.

Point Transformations and Relationships among Linear Anomalous Diffusion, Normal Diffusion and the Central Limit Theorem

We present new connections among linear anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem (CLT). This is done by defining a point transformation to a new position variable, which we postulate to be Cartesian, motivated by considerations from super-symmetric quantum mechanics. Canonically quantizing in the new position and momentum variables according to Dirac gives rise to generalized negative semi-definite and self-adjoint Laplacian operators. These lead to new generalized Fourier transformations and associated probability distributions, which are form invariant under the corresponding transform. The new Laplacians also lead us to generalized diffusion equations, which imply a connection to the CLT. We show that the derived diffusion equations capture all of the Fractal and Non-Fractal Anomalous Diffusion equations of O’Shaughnessy and Procaccia. However, we also obtain new equations that cannot (so far as we can tell) be expressed as examples of the O’Shaughnessy and Procaccia equations. The results show, in part, that experimentally measuring the diffusion scaling law can determine the point transformation (for monomial point transformations). We also show that AD in the original, physical position is actually ND when viewed in terms of displacements in an appropriately transformed position variable. We illustrate the ideas both analytically and with a detailed computational example for a non-trivial choice of point transformation. Finally, we summarize our results.

Deriving of the Generalized Special Relativity (GSR) by Using Mirror Clock and Lorentz Transformations

Einstein relativity theory shows its high capability of promoting itself to solve the long stand physical problems. The so-called generalized special relativity (GSR) was derived later, using the beautiful Einstein relation between field and space-time curvature. In this work we re-derive (GSR) expression of time by incorporating the field effect in it, and by using mirror clock and Lorentz transformations. This expression reduces to that of (GSR) the previous conventional one, besides reducing to special relativistic expression. It also shows that the speed of light is constant inside the field and is equal to C. This means that the observed decrease of light in matter and field is attributed to the strong interaction of photons with particles and mediates which causes successive absorption and reemission processes that lead to time delay. This absorption process makes some particles appear to move faster than light within the field or medium. This new expression, unlike that of GSR, can describe time and coordinate relativistic expressions for strong as well as weak fields at constant acceleration.

Dynamic Electropulsing Induced Phase Transformations and Their Effects on Single Point Diamond Turning of AZ91 Alloy

The effects of dynamic electropulsing on microstructure changes and phase transformations of a rolled Mg-9Al-1Zn alloy were studied by using optical microscopy, X-ray diffraction, back-scattered scanning microscopy and transmission electron microscopy techniques. The decomposition of β phase was accelerated under dynamic electropulsing, compared with the conventional thermal processes. Dynamic electropulsing was less effective in affecting the phase transformations, but more effective in reducing residual stress than the static electropulsing. Dynamic electropulsing improved machinability of single point diamond turning, the mechanism of which is discussed from the point of view of dislocation dynamics.

YANG-BAXTER OPERATORS AND TENSOR TRANSFORMATIONS

The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transformations over the category of modules of a Yang-space form a group.

Symmetry transformations for magnetohydrodynamics and Chew–Goldberger–Low equilibria revisited

We generalize the symmetry transformations for magnetohydrodynamic(MHD) equilibria with isotropic pressure and incompressible flow parallel to the magnetic field introduced by Bogoyavlenskij in the case of the respective Chew–Goldberger–Low(CGL) equilibria with anisotropic pressure. We find that the geometrical symmetry of the field-aligned equilibria can be broken by those transformations only when the magnetic field is purely poloidal. In this situation we derive three-dimensional CGL equilibria from given axisymmetric ones. Also, we examine the generic symmetry transformations for MHD and CGL equilibria with incompressible flow of an arbitrary direction, introduced in a number of papers, and find that they cannot break the geometrical symmetries of the original equilibria, unless the velocity and magnetic field are collinear and purely poloidal.

PHASE TRANSFORMATIONS IN Ti-10V-2Fe-3Al NEAR β-ALLOY DURING AGING

The phase transformations in Ti-10V-2Fe-3AI alloy during aging have been studied bymeans of X-ray diffraction and TEM techniques.The morphology and distribution of precipi-tated phases were examined.The lattice parameters of α and β phases as a function of the ag-ing time is obtained,the hardness variation of the specimens related to the aging temperatureand time has been given as well.

Double reversible transformations under various treatment states

The double reversible transformations at low temperature in CuZnAlMnNi shape memory alloy were investigated by differential scanning calorimetry. It is found that the transformations occur not only in the as quenched sample, but also in the as trained, as aged and as thermal cycled samples, and various treatments give rise to different influences on the transformation temperatures of the two transformations. Though the temperature interval between the two transformation peaks increases after training, aging and thermal cycling, the initial temperature of the M → A transformation is just the final temperature of the X → M transformation, namely, the X → M transformation is immediately followed by the M → A transformation upon heating.

Tensile Stress Induced Phase Transformations in Zn-Al Alloy

Both furnace cooled and as-cast eutectoid Zn-Al alloys were investigated under external tensile stress at 100℃. It was observed that the external tensile stress caused decomposition of two metastable phases η’T and η’S which derived from both original state of the alloy, and a phase transformation, αf +ε→T’ +η， in both furnace cooled and as-cast eutectoid Zn-Al alloys. Also spheroidized structure formed partially during tensile testing. Superplasticity of the alloy has been discussed correlating with the phase transformations and microstructural changes.

Gershgorin and Rayleigh Bounds on the Eigenvalues of the Finite-Element Global Matrices via Optimal Similarity Transformations

The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.

Thoughts on Transformations in International Finance

Asuccession of shock waves from international financial crisis has revealed pro-found transformations in the power balance of international finance,which willredraw the global financial landscape and exert a tremendous impact on the worldconfiguration in the next century.A scramble is on among major powers for com-manding heights in the new financial scene through strategic adjustments.Chinashould seize the opportunity to seek a niche for itself in this emerging world map,while guarding against risks in the defense of national economic security.

Multipliers and Classification of m-Möbius Transformations

It is known that any m-Möbius transformation is an ordinary Möbius transformation in every one of its variables when the other variables do not take the values a and 1/a, where a is a parameter defining the respective m-Möbius transformation. For ordinary Möbius transformations having distinct fixed points, the multiplier associated with one of these points completely characterizes the nature of that transformation, i.e. it tells us if it is elliptic, hyperbolic or loxodromic. The purpose of this paper is to show that fixed points exist also for m-Möbius transformations and multipliers associated with them can be computed as well. As in the classical case, the values of those multipliers describe completely the nature of the transformations. The method we used was that of a thorough study of the coefficients of the variables involved, with which occasion we discovered surprising symmetries. These were the results allowing us to prove the main theorem regarding the fixed points of a m-Möbius transformation, which is the key to further developments. Finally we were able to illustrate the geometric aspects of these transformations, making the whole theory as intuitive as possible. It was as opening a window into a space of several complex variables. This allows us to prove that if a bi-Möbius transformation is elliptic or hyperbolic in z1 at a point z2 it will remain the same on a circle or line passing through z2. This property remains true when we switch z1 and z2. The main theorem, dealing with the fixed points of an arbitrary m-Möbius transformation made possible the extension of this result to these transformations.