Miracle-dz/UniFAR-FTUs huggingface dataset:
Constructive Approaches to Biorthogonal Finitely Supported Ternary Wavelets and Wavelet Wraps

In this paper, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelets is proposed. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A novel constructive method for designing a sort of biorthogonal vector-valued wavelet wraps is presented and their biorthogonality traits are characerized. Two biorthogonality formulas regarding these wavelet wraps are established.
COINTEGRATION AND COMMON FACTORS

Alternative common factors representations for cointegrated vectors are studied. It is shown that dynamic factor models produce as particular cases the alternative common trend representations for cointegrated variables available in the literature, including the one of Stock and Watson(1988). Furthermore, it is proved that common factor representations with I(1) components imply cointegration. A more efficient procedure for fmding the numbers of cointegrated vectors based on this dynamic factors model is suggested.
On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model

Abstract The seminal paper by Gerber and Shiu (1998) unified and extended the study of the event of ruin and related quantities, including the time at which the event of ruin occurs, the deficit at the time of ruin, and the surplus immediately prior to ruin. The first two of these quantities are fundamentally important for risk management techniques that utilize the ideas of Value-at-Risk and Tail Value-at-Risk. As is well known, calculation of these and related quantities requires knowledge of the associated probability distributions. In this paper we derive an explicit expression for the joint (defective) distribution of the time to ruin, the surplus immediately prior to ruin, and the deficit at ruin in the classical compound Poisson risk model. As a by-product, we obtain expressions for the three bivariate distributions generated by the time to ruin, the surplus prior to ruin, and the deficit at ruin. Finally, we consider mixed Erlang claim sizes and show how the joint (defective) distribution of the t.
Towards optimal functional representation of head-related transfer functions in the horizontal plane

Head-related transfer function (HRTF) individualization using principle component analysis (PCA) modelling rely on the empirical data to reduce HRTF dimensionality for an optimal representation and to achieve HRTF personalization by tuning the model weights with the subject anthropometric parameters. However, for these representations, the basis is discrete and data dependent which can limit its usefulness in universal HRTF representation. This paper studies the optimal functional representation of magnitude HRTF of 45 subjects for sound sources in the horizontal plane. We firstly use circular harmonics to extract the subject-independent HRTF angular dependence. The remaining spectral components of 45 subjects are then modelled by PCA and two standard functions, i.e., Fourier series and Fourier Bessel series. The metric to evaluate the model efficiency is the expansion weights cumulative variance. We identify that individual magnitude HRTFs over 20 kHz range could be modelled adequately well by a linear c.
A resolution procedure based on a fuzzy logic

As the use of non-classical logics become increasingly important in computer science, artificial intelligence and logic programming, the development of efficient automated theorem proving based on non-classical logic is currently an active area of research. The paper aims at the resolution principle for the Pavelka type fuzzy logic. Pavelka had shown in 1979 that the only natural way of formalizing fuzzy logic for truth values in the unit interval [0, 1] is by using Lukasiewicz's implication operator, in short L/sub /spl aleph//. So we firstly focus on the resolution principle for Lukasiewicz logic L/sub /spl aleph//. Some limitations of classical resolution and resolution procedures for some fuzzy logics are analyzed. Then some preliminary ideals about combining resolution procedure with the implication connectives in L/sub /spl aleph// are given. Moreover, a resolution-like rule, i.e., MP rule is proposed. By use of the MP rule, a resolution procedure in L/sub /spl aleph// is proposed and the soundness theorem of this resolution procedure is also proved. Finally, we apply the resolution to a Horn clause with truth-value in an enriched residuated lattice as Pavelka (1979) discussed.
Optimal placement of mobile sensors for data assimilations

ABSTRACT We explore the theoretical framework as well as the associated algorithms for the problem of optimally placing mobile observation platforms to maximise the improvement of estimation accuracy. The approach in this study is based on the concept of observability, which is a quantitative measure of the information provided by sensor data and user-knowledge. To find the optimal sensor locations, the observability is maximised using a gradient projection method. The Burgers equation is used to verify this approach. To prove the optimality of the sensor locations, Monte Carlo experimentations are carried out using standard 4D-Var algorithms based on two sets of data, one from equally spaced sensors and the other from the optimal sensor locations. The results show that, relative to equally spaced sensors, the 4D-Var data assimilation achieves significantly improved estimation accuracy if the sensors are placed at the optimal locations. A robustness study is also carried out in which the error covariance matrix is varied by 50% and the sensor noise covariance is varied by 100%. In addition, both Gaussian and uniform probability distributions are used for the sensor noise and initial estimation errors. In all cases, the optimal sensor locations result in significantly improved estimation accuracy.
Faddeev-Jackiw Quantization of Non-Abelian Systems

The Faddeev and Jackiw procedure for the quantization of constrained gauge systems is used on the analysis of non-Abelian symmetries. The key point is that the gauge algebra of the non-Abelian constraints under generalized brackets can be reconstructed. This follows from the singular matrix that defines the basic geometric structure of the model and its corresponding zero-modes. The attainment of this algebra, not previously found in the Faddeev-Jackiw formalism for constrained theories, leads to the correct transformation properties for the gauge fields. This construction shows that the zero-modes of the symplectic matrix and the generators of gauge symmetry are closely related. To illustrate the method studied here we consider a simple mechanical model with an underlying non-Abelian symmetry and the field theory of pure Chern-Simons theory in (2+1) dimensions.
Multiwavelength FLIM: new applications and algorithms

The combination of time-resolved and spectral resolved techniques as achieved by SLIM (spectrally resolved fluorescence lifetime imaging) improves the analysis of complex situations, when different fluorophores have to be distinguished. This could be the case when endogenous fluorophores of living cells and tissues are observed to identify the redox state and oxidative metabolic changes of the mitochondria. Other examples are FRET (resonant energy transfer) measurements, when different donor/acceptor pairs are observed simultaneously. SLIM is working in the time domain employing excitation with short light pulses and detection of the fluorescence intensity decay in many cases with time-correlated single photon counting (TCSPC). Spectral resolved detection is achieved by a polychromator in the detection path and a 16-channel multianode photomultiplier tube with the appropriate routing electronics. Within this paper special attention will be focused on FRET measurements with respect to protein interactions in Alzheimers disease. Using global analysis as the phasor plot approach or integration of the kinetic equations taking into account the multidimensional datasets in every spectral channel we could demonstrate considerable improvement of our calculations.
Optical frequency response analysis of light-emitting transistors under different microwave configurations

In this report, the optical frequency responses of InGaP/GaAs heterojunction bipolar light-emitting transistors are measured and analyzed using electrical small-signal equivalent circuit models under common-emitter, common-base, and common-collector configurations. Different optical modulation amplitudes and bandwidths, f3 dB, are obtained due to different input impedances and electrical transfer functions. The optical response of light-emitting transistors is able to be “tuned” by different input ports due to unique three-terminal characteristics along with carrier-photon conversion in the base region. From microwave analyses, identical “intrinsic” optical responses can be determined under three configurations at same DC bias condition.
Clues to the existence of deterministic chaos in river flow

The present work investigates the existence of a component of deterministic chaos in the discharge time series of a river. The first part of the work is concerned with the reconstruction of the attractor and the calculation of the correlation integral; in the second part the analysis is conducted with the aid of nonlinear prediction. Some clues emerge as to the possible presence of chaos, probably immersed in a phenomenon altogether more extensive and manifold. If confirmed, this presence could provide interesting openings for a better comprehension of the formation mechanism of river flow, and a more precise forecasting of floods.
The Volterra and Wiener Theories of Nonlinear Systems

This text presents a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, thus yielding new insights and a better comprehension of the subject. The Volterra and Wiener theories are useful in the study of systems in biological, mechanical, and electrical fields.
A Technique for Computing Vertical Transports by Precipitating Cumuli

Abstract A method is described for calculating cumulus-scale vertical transports of mass, sensible heat and hori-zontal momentum from detailed measurements of precipitation. The basic premises are that the amount of lifting in a cumulus cell is related to the precipitation which it produces and that the temperature excess and entrainment are reflected in its vertical development. The amount of cellular precipitation may be obtained from quantitative radar data or high-resolution rain gauge records, the cell depths from radar and radiosonde data. The mass of air transported upward within the cells is computed from the conservation of water given the amount of cellular precipitation. A relationship between measured cellular rain and condensate within cumulus cells is based on available empirical information. Entrainment rate and the shape of the mass transport curve as a function of height are specified in a manner consistent with physical considerations, experimental evidence, and one-dimensional dynamic m.
Silicon-on-insulator devices for high voltage and power IC applications

Silicon-on-insulator (SOI) technology based on wafer bonding promises to deliver significant performance advantages and cost reduction over the existing bulk silicon technologies used for making power integrated circuits. A review is presented of the fundamental considerations that arise in the study of SOI devices for high-voltage applications. Significant device design parameters, such as the off-state breakdown voltage, on-state specific resistance, thermal dissipation, packing density, and manufacturability are discussed in the context of the applicable device physics and SOI material requirements. Several possible approaches for achieving high breakdown voltages in SOI devices are described. The advantages and limitations of each approach are discussed and illustrated with some recent results on experimental devices.
Characterizing Two-Dimensional Maps Whose Jacobians Have Constant Eigenvalues

Abstract Recent papers have shown that ${{C}^{1}}$ maps $F:\,{{\mathbb{R}}^{2}}\,\to {{\mathbb{R}}^{2}}$ whose Jacobians have constant eigenvalues can be completely characterized if either the eigenvalues are equal or $F$ is a polynomial. Specifically, $F\,=\,(u,\,v)$ must take the form $$u\,=\,ax\,+\,by\,+\,\beta \phi (\alpha x\,+\,\beta y)\,+\,e$$ $$v\,=\,cx\,+\,dy\,-\,\alpha \phi \,(\alpha x\,+\,\beta y)\,+\,f$$ for some constants $a,\,b,\,c,\,d,\,e,\,f,\,\alpha ,\,\beta $ and a ${{C}^{1}}$ function $\phi $ in one variable. If, in addition, the function $\phi $ is not affine, then 1 $$\alpha \beta (d\,-\,a)\,+\,b{{\alpha }^{2}}\,-\,c{{\beta }^{2}}\,=\,0. $$ This paper shows how these theorems cannot be extended by constructing a real-analytic map whose Jacobian eigenvalues are $\pm 1/2$ and does not fit the previous form. This example is also used to construct non-obvious solutions to nonlinear PDEs, including the Monge—Ampère equation.
The Principal Constituent of the Tides in the English and Irish Channels

1. A chart of co-tidal and co-range lines for the North Sea was prepared at the Tidal Institute in the year 1923, and the methods then used have now been further developed and improved and applied to the English Channel, the Irish Sea, and their approaches. The methods used depend largely upon the known dynamical equations connecting the currents with the gradients of the elevations. If any assumption be made as to the values of the range of tide and the relative phases of the elevation and currents, then we can deduce from this information at one station, not only the directions of the co-tidal and co-range lines at that point, but also the degree of separation of the lines for any given unit of phase or range. This criterion, applied to speculative charts hitherto published, suffices at once either to verify or to condemn the charts. Again, without any assumptions at all, from the gradients at a number of stations on a line of small curvature, starting at a point at which the elevation is known, the elevations at all points along the line can be computed by simple methods of numerical integration.
Abstract Geometric Crossover for the Permutation Representation

Abstract crossover and abstract mutation are representation-independent operators that are well-defined once a notion of distance over the solution space is defined. They were obtained as generalization of genetic operators for binary strings and real vectors. In this paper we explore how the abstract geometric framework applies to the permutation representation. This representation is challenging for various reasons: because of the inherent difference between permutations and the representations that inspired the abstraction; because the whole notion of geometry over permutation spaces radically departs from traditional geometries and it is almost unexplored mathematical territory; because the many notions of distance available and their subtle interconnections make it hard to see the right distance to use, if any; because the various available interpretations of permutations make ambiguous what a permutation represents, hence, how to treat it; because of the existence of various permutation-like representations that are incorrectly confused with permutations; and finally because of the existence of many mutation and recombination operators and their many variations for the same representation. This article shows that the application of our geometric framework naturally clarifies and unifies an important domain, the permutation representation and the related operators, in which there was little or no hope to find order. In addition the abstract geometric framework is used to improve the design of crossover operators for well-known problems naturally connected with the permutation representation.
Multi-Valued Reasoning about Reactive Systems

Traditional computer science is Boolean: a Turing machine accepts or rejects its input, and logic assertions are true or false. A primary use of logic in computer science has been the specification and verification of reactive systems. There, desired behaviors of systems are formally specified by temporal-logic formulas, and questions about systems and their behaviors are reduced to questions like satisfiability and model checking. While correctness is binary, many questions we want to ask about systems are multi-valued. The multi-valued setting arises directly in systems in with quantitative aspects, for example systems with fuzzy assignments or stochastic dynamics, and arises also in Boolean systems, where it origins from the semantics of the specification formalism. In particular, beyond checking whether a system satisfies its specification, we may want to evaluate the quality in which the specification is satisfied. The term “quality” may refer to many aspects of the behavior: we may want to prioritize different satisfaction alternatives, refer to delays, costs, and many more. In recent years, we have seen a growing effort in the formal-method community to shift from Boolean specification formalisms to multi-valued ones.
Soil erosion estimation using remote sensing techniques in theshirvan plain of the republic of Azerbaijan

Soil erosion is one of the major environmental problems in terms of soil degradation in the Shirvan plain of the Republic of Azerbaijan. Soil erosion leads to significant on- and off-site impacts such as significant decrease in the productive capacity of the land and sedimentation. The key aspects influencing the quantity of soil erosion mainly rely on the vegetation cover, topography, soil type, and climate. This research studies the quantification of soil erosion under different levels of data availability in the Shirvan plain. Remote sensing (RS) and Geographic Information System (GIS) techniques have been implemented for the assessment of the data, applying the Revised Universal Soil Loss Equation (RUSLE) for the calculation of the risk of erosion. Thirty soil samples were randomly selected for the calculation of the erodibility factor, based on calculating the 𝐾-factor values derived from soil property surfaces after interpolating soil sampling points. Soil erosion risk map was reclassified into five erosion risk classes and 25.3% of the Shirvan plain is under severe risk (190,740 ha). GIS and RS proved to be powerful instruments for mapping soil erosion risk, providing sufficient tools for the analytical part of this research. The mapping results certified the role of RUSLE as a decision support tool.
D-Branes on Calabi-Yau Spaces

In this thesis the properties of D-branes on Calabi–Yau spaces are investigated. Compactifications of type II string theories on these spaces to which D-branes are added lead to N = 1 supersymmetric gauge theories on the world-volume of these D-branes. Both the Calabi–Yau spaces and the D-branes have in general a moduli space. We examine the dependence of the gauge theory on the choice of the moduli, in particular those of the K¨ahler structure of the Calabi–Yau manifold. For this purpose we choose two points in this moduli space which are distinguished by the fact that there exists an explicit description of the spectrum of the D-branes. One of these points corresponds to a manifold in the large volume limit on which the D-branes are described by classical geometry of vector bundles. At the other points the size of the manifold is smaller than its quantum fluctuations such that the classical geometry looses its meaning and has to be replaced by a conformal field theory. The Witten index in the open string sector is independent of the variation of these moduli and serves, together with mirror symmetry, as a tool to compare the two descriptions. We give an extensive and general presentation of these two descriptions for the class of Fermat hypersurfaces in weighted projective spaces. We explicitly carry out the comparison in many representative examples. Among them are manifolds admitting elliptic and K3-fibrations and manifolds whose moduli space can be embedded into the moduli space of another manifold. One main focus is on D4-branes, in particular on the dimension of their moduli space. Using the methods developed we are able to further confirm with our results the modified geometric hypothesis by Douglas. It essentially states that the properties of these D-branes or of these gauge theories can be determined partly by classical geometry, partly by mirror symmetry. A peculiarity of these gauge theories is the appearance of lines of marginal stability at which BPS states can decay. We show the existence of such lines in the framework of this class of Calabi–Yau spaces in two di®erent ways and discuss the connection to the formation of bound states. Of particular interest is the D0-brane whose appearance in this framework is explained.
Layer‐wise attribution of vertical motion and the influence of potential‐vorticity anomalies on synoptic development

A methodology is presented for attributing vertical motion to potential vorticity (PV) in a explicit manner using the quasi‐geostrophic omega equation. The methodology is then used to determine the contribution individual PV anomalies make to the synoptic development. It is shown how the total vertical motion may be decomposed into self‐generating and interaction terms. The former correspond to vertical motion that arises from one PV region alone, whilst each of the interaction terms represent vertical motion due to the interaction of two different regions of PV. The method is applied to a number of cyclones studied in the Fronts and Atlantic Storm‐Tracks Experiment in order to determine the dynamical role of individual PV regions in cyclogenesis. For purposes of comparison, cyclones were chosen to be representative of the types (A, B and C) of an extended Petterssen–Smebye scheme devised by Deveson, Browning and Hewson. In terms of our new PV method, the Type A and B cyclones exhibit only subtle differences, with the upper‐level layer of PV playing a larger role in the case of the Type B cyclone. A much larger difference is apparent between the Type A and B cyclones on the one hand, and the Type C cyclone on the other: in the Type C cyclone, the upper‐level PV self‐generating term plays an important role, whereas in the Type A and B cases the influence of the upper‐level PV is largely restricted to the interaction terms. In all of the cases, the vertical motion attributable to the interaction between the low‐level PV and boundary thermal gradient was found to be large. Hence, from the viewpoint of instantaneous attribution, we conclude that the low‐level PV is always important. Copyright © 2003 Royal Meteorological Society