Translational Theorem Research Articles

A Generalization of the Brouwer Plane Translation Theorem

We show that if an orientation-preserving homeomorphism of the plane has a topologically chain recurrent point, then it has a fixed point, generalizing the Brouwer plane translation theorem.

Pergeseran Penerjemahan dalam Penerjemahan Manga "Kimi No Ga Daidaidaidaidai Suki Na 100-Nin No Kanojo"

This study is focused into shift in translation, to study the shift in the English translation translation of “Kimi no Koto ga Daidaidaidaidai Suki na 100-nin no Kanojo” manga. In translation process, there is text that can be directly translated into target language, but sometimes it needs to be adjusted or omitted by changing the phrase, clause, or sentence which is called shift in translation. Specifically, in a language where the grammatical structure differs from each other’s. For example, Japanese with Indonesian. The data will be identified utilizing Catford’s shift in translation theorem. With qualitative methods the data will be analyzed from the conversations between characters. This study discovers five types of shifts, which is: (1) level shift that occurs when the lexical and grammatical meaning from translation differs; (2) structure shift that occurs if the order of grammatical structure is different; (3) word class shift that occurs when the word class change for example from verb into noun; (4) unit shift that occurs when the phrase becomes clause, clause into sentence, etc. And lastly (5) intra system shift that occurs when the grammatical structure cause the translation to shift.

Conditional wiener integral associated with Gaussian processes and applications

Let C0[0,T] denote the one-parameter Wiener space and let C?0[0,T] be the Cameron-Martin space in C0[0,T]. Given a function k in C?0[0,T], define a stochastic process Zk : C0[0,T] ? [0, T] ? R by Zk(x, t) = R t 0 Dk(s)dx(s), where Dk ? d/dt k. Let a random vector XG,k : C0[0,T] ? Rn be given by XG,k(x) = ((g1,Zk(x,?))~,..., (gn,Zk(x,?))~), where G = {g1, ..., gn} is an orthonormal set with respect to the weighted inner product induced by the function k on the space C?0[0,T], and (g,Zk(x,?))~ denotes the Paley-Wiener-Zygmund stochastic integral. In this paper, using the reproducing kernel property of the Cameron-Martin space, we establish a very general evaluation formula for expressing conditional generalized Wiener integrals, E(F(Zk(x,?)) |XG,k(x) = ??), associated with the Gaussian processes Zk. As an application, we establish a translation theorem for the conditional Wiener integral and then use it to obtain various conditional Wiener integration formulas on C0[0,T].

Membrane sound absorber with a granular activated carbon infill

An impervious membrane sound absorber with an air cavity partially filled with a porous material is a viable alternative to perforated panels when impermeable surfaces are required. On the other hand, due to its unusually high sound absorption properties at low frequencies, using activated carbon (AC) in granular form as an absorbing material has recently received attention. This paper reports the sound absorption performance of a novel system consisting of a thin stretched impervious circular membrane made of silicone, backed by an air cavity partially filled with granular AC. The system is analyzed theoretically using the impedance translation theorem. The normal-incidence sound absorption was measured in an impedance tube for combinations of cavity depth, membrane tension, and membrane surface density. The results of using an AC and a fiberglass infill material of the same thickness in the air cavity were also compared. The findings validated the advantage of AC as porous infill material of a membrane sound absorber in the low-frequency range. Furthermore, the outcomes of the impedance tube experiments were in good agreement with theoretical predictions. The findings reported in this work could be used to design new innovating sound-absorbing metamaterials based on activated carbon and stretched membranes.

A novel kinematics and statics correction algorithm of semi-cylindrical foot end structure for 3-DOF LHDS of legged robots

In this paper, aiming at the problem that the ideal modeling point of the foot end deviates from the actual contact point due to the rolling effect of the semi-cylindrical foot end in leg hydraulics drive system (LHDS), a novel and relatively simple kinematics and statics correction algorithm is proposed. This algorithm can effectively improve the accuracy of LHDS kinematics and statics, and it is still applicable when the body and the contact surface are at different angles. Firstly, this paper deduces the kinematics and statics when the foot end of LHDS is regarded as the point foot, analyzes and calculates the deviation under common working conditions. Secondly, in view of this phenomenon, a kinematics correction algorithm based on virtual DOF and a statics correction algorithm based on translation theorem of forces are proposed respectively. Finally, the proposed algorithm is verified by LHDS performance test platform under various working conditions. The results show that after applying the kinematics correction algorithm, the trajectory deviation reduction rate of the hip joint is over 65%; after applying the statics correction algorithm, the deviation reduction rate of foot end contact force is over 43%. The related research results can be applied to any similar foot end, which has engineering application value.

Solving one-dimensional acoustic systems using the impedance translation theorem and equivalent circuits: A graduate level homework assignment.

The natural frequency resonances and sound radiation from one-dimensional acoustic systems are of great interest in the study of musical instruments, human vocal tract effects on speech, automotive exhaust pipes, duct systems for temperature control in buildings, and more. The impedance translation theorem is an approach that may be used to solve for the input impedance and therefore the resonance frequencies of one-dimensional systems. Equivalent circuits offer another approach to solving one-dimensional systems, though with equivalent circuits you can also solve for the response at any location in the system, including the radiated sound pressure. At Brigham Young University, there are two graduate level courses that teach these two techniques. One of the most challenging and memorable homework assignments from these courses is based on using one of these techniques to analyze a particular acoustic system and compare its response with the real thing. This paper discusses the basics of these two techniques and applies them to an analysis of phonemes produced by altering the human vocal tract. Details about the homework assignments are also given.

Generalized sequential Feynman integral and Fourier–Feynman transform

We introduce the concepts of a generalized sequential Feynman integral and a generalized sequential Fourier–Feynman transform. Existence theorems of these integral and transform are obtained for functionals in a Banach algebra 𝒮^ and some related functionals. Also we give a simple proof of a translation theorem for generalized sequential Feynman integral. Previous results on sequential Feynman integral and sequential Fourier–Feynman transform can be obtained as corollaries of our results. In the last section we introduce the concept of translation invariant generalized sequential Feynman integral.

One problem, two solution approaches: Using the impedance translation theorem and equivalent circuits for graduate level homework

Research applications such as the study of musical instruments, human vocal tract effects on speech, automotive exhaust pipes, HVAC ducts, and others often utilize one-dimensional models of the acoustic systems to determine the resonance behavior and sound radiation properties. The impedance translation theorem and the equivalent circuits method both include all the physics associated with these one-dimensional systems, although one approach or the other may be more appropriate or straightforward to use depending on the result desired. Both these methods are taught at Brigham Young University in two graduate level courses. One of the most challenging and memorable homework assignments from each of these courses is based on using these techniques to analyze a particular acoustic system and compare its response with the real thing. This paper will overview these two techniques and outline how they are applied in homework assignments for these two courses to analyze phonemes produced by altering the human vocal tract.

Some translation theorems in bipolar valued multi fuzzy subnearring of a nearring

Some translation theorems in bipolar valued multi fuzzy subnearring of a nearring

An extension of the Cameron–Martin translation theorem via Fourier–Hermite functionals

In this paper, we use the Fourier–Hermite functionals to extend the structure of the Cameron–Martin translation theorem on an abstract Wiener space $$(H,B,\nu )$$ . The directional function in our translation theorem may not be in the Cameron–Martin subspace H of B. We then proceed to obtain an explicit formula for our general translation theorem.

Analysis of high speed bearing based on virtual rods model

The traditional high-speed ball bearing analysis is based on the quasi-static model proposed by Jones-Harris (J-H). This study gives another bearing analysis model based on the relative position of the ball center and the centers of curvature of the raceway grooves, described by the virtual rods. Specifically, the load and deformation of the virtual rods are determined according to the principle of force transmissibility, the translation theorem of a force, and elastic-contact deformation between steel ball bearings and raceway grooves. And the iterative variables such as the axial, radial and angular deformations are gradually introduced into the calculation model to solve the force and kinematic parameters under pure axial load, bidirectional and tri-directional combined loads. The correctness of the virtual rods model is verified by the contact angle for axial and bidirectional load. The influence of gyroscopic moment and raceway grooves control parameter on the actual contact angle under tridirectional loading conditions are calculated and analyzed respectively. The proposed model uses fewer equations and lower-dimension parameters than those used by the traditional highspeed ball bearing analysis method, improves the solution rate of the equations.

The Existence of Random Attractor for Stochastic Suspension Bridge Equation

This paper is aimed at an extensible suspension bridge equation with additive noise and linear memory. For the suspension bridge equations without additive noise and memory, there are many classical results. However, the extensible suspension bridge equations with both additive noise and linear memory were not studied before. The object of this paper is to provide a result on the random attractor to the above problem using compactness translation theorem and decomposition technique.

Fundamental formulas for modified generalized integral transforms

Various fundamental formulas and results for integral transforms on a function space have been studied in many papers. However, there are many limitations with regard to obtaining the fundamental formulas and results with respect to integral transforms on the function space, because generalized Brownian motion has the nonzero mean function. Despite recent attempts address this problem, it has yet to be resolved. In this paper, based on the definitions of the modified generalized integral transform and (generalized) convolution product on function space, we establish the fundamental formulas relating the two. The fundamental formulas obtained via the translation theorem are applied in several examples to demonstrate the usefulness of our fundamental approach.

A Modified Analytic Function Space Feynman Integral of Functionals on Function Space

In this paper, the authors introduce a class of functionals. This class forms a Banach algebra for the special cases. The main purpose of this paper is to investigate some properties of the modified analytic function space Feynman integral of functionals in the class. Those properties contain various results and formulas which were not obtained in previous papers. Also, the authors establish some relationships involving the first variation via the translation theorem on function space. In particular, the authors establish the Fubini theorem for the modified analytic function space Feynman integral which was not obtained in previous researches yet.

Application of Equivalence Principle for EM Scattering From Irregular Array of Arbitrarily Oriented PEC Scatterers Using Both Translation and Rotation Addition Theorems

Electromagnetic scattering from irregular array of arbitrarily oriented PEC scatterers is investigated using a novel domain decomposition method based on equivalence principle algorithm (EPA) in conjunction with addition theorems for spherical wave harmonics (SWHs). Each element is considered to be enclosed by a spherical equivalence surface as a single domain. The primary unknowns on each element are replaced by the equivalent electric and magnetic current distributions on the equivalence sphere in terms of RWG basis functions. From these current distributions, the scattered field outside its equivalence sphere is evaluated in terms of SWHs in the local coordinates system fixed to each element body. The SWHs in rotated local coordinates are translated as a new set of SWHs in other local coordinates with the same origin but axes parallel to the global coordinate’s axes using the rotation addition theorem. Furthermore, the mutual coupling effects among the separated domains are considered using the translation addition theorem for parallel local coordinate systems. It is shown that the proposed method effectively reduces the computational costs by reducing the number of unknowns versus the conventional EPA. The efficiency and validity of the proposed method are investigated through several numerical examples.

Translation Theorem for Function Space Integral Associated with Gaussian Paths and Applications

In this paper we establish a more general translation theorem for function space integral associated with Gaussian paths on the function space $$C_{a,b}[0,T]$$ . The function space $$C_{a,b}[0,T]$$ is induced by a generalized Brownian motion process. Thus, the Gaussian processes used in this paper are non-centered processes. We next apply our fundamental translation theorem to the generalized Fourier–Feynman transforms. We then proceed to show that these general translation theorems for the generalized Fourier–Feynman transforms can be applied to two well-known classes of functionals on the function space $$C_{a,b}[0,T]$$ .

Translation theorems for the Fourier–Feynman transform on the product function space $C_{a,b}^{2}[0,T

In this article, we establish the Cameron–Martin translation theorems for the analytic Fourier–Feynman transform of functionals on the product function space C a , b 2 [ 0 , T ] . The function space C a , b [ 0 , T ] is induced by the generalized Brownian motion process associated with continuous functions a ( t ) and b ( t ) on the time interval [ 0 , T ] . The process used here is nonstationary in time and is subject to a drift a ( t ) . To study our translation theorem, we introduce a Fresnel-type class F A 1 , A 2 a , b of functionals on C a , b 2 [ 0 , T ] , which is a generalization of the Kallianpur and Bromley–Fresnel class F A 1 , A 2 . We then proceed to establish the translation theorems for the functionals in F A 1 , A 2 a , b .

Time-dependent asymptotic behavior of the solution for wave equations with linear memory

In this article, we consider the long-time behavior of solutions for the wave equation with linear memory. Within the theory of process on time-dependent spaces, we investigate the existence of the time-dependent attractor by using the operator decomposition technique and compactness of translation theorem and more detailed estimates. Furthermore, the asymptotic structure of time-dependent attractor, which converges to the attractor of parabolic equation with memory, is proved. Besides, we obtain a further regular result about ut.

On the Relation between Reactive Synthesis and Supervisory Control of Input/Output Behaviours

Reactive synthesis (RS) and supervisory control theory (SCT) both provide a design methodology for digital systems. RS takes a computer science perspective and seeks to synthesise a system that interacts with its environment in computation cycles and which, doing so, satisfies a prescribed specification. SCT takes a control theoretic perspective and seeks to synthesise a controller that - in closed-loop configuration with a plant - enforces a prescribed specification, where all dynamics are driven by discrete events. While both synthesis techniques seem superficially very similar, their technical details differ significantly. We provide a formal comparison allowing us to identify conditions under which one can solve one synthesis problem via the other one and we discuss how the resulting solutions compare. To facilitate this comparison, we give a unified introduction to RS and SCT and derive formal problem statements and a characterisation of their solutions in terms of ω-languages. As recent contributions to the two fields focus on different aspects of the respective problem, our translational theorems can be used to guide the application of algorithmic techniques from one field in the other.

On The Degenerate Laplace Transform-I

We make an attempt in this paper to extend the very recent work of Kim and Kim [24] on degenerate Laplace transform. Using the definition of the degenerate Laplace transform as given by Kim and Kim [24] and some of the results developed by them in this study we prove the first and second translation theorems and the change of scale property for the degenerate Laplace transform and give some illustrations highlighting the applications of these results for the degenerate Laplace transform of a function.