scholarly journals Prolegomena to an Operator Theory of Computation

Information ◽  
2020 ◽  
Vol 11 (7) ◽  
pp. 349
Author(s):  
Mark Burgin ◽  
Gordana Dodig-Crnkovic
Keyword(s):  
Data Structures ◽  
Category Theory ◽  
Operator Theory ◽  
Theoretical Studies ◽  
Theory Of Computation ◽  
Information Dynamics ◽  
Practical Applications ◽  
Theory Of Computing ◽  
Processing Information ◽  
The Difference

Defining computation as information processing (information dynamics) with information as a relational property of data structures (the difference in one system that makes a difference in another system) makes it very suitable to use operator formulation, with similarities to category theory. The concept of the operator is exceedingly important in many knowledge areas as a tool of theoretical studies and practical applications. Here we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, processes, and their networks.

scholarly journals Modeling Computing Devices and Processes by Information Operators

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 18
Author(s):  
Mark Burgin ◽  
Gordana Dodig-Crnkovic
Keyword(s):  
Operator Theory ◽  
Computer Architectures ◽  
General Context ◽  
Theoretical Studies ◽  
Operator Approach ◽  
Operator Representation ◽  
Practical Applications ◽  
Theory Of Computing

The concept of operator is exceedingly important in many areas as a tool of theoretical studies and practical applications. Here, we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, networks, and processes. In particular, the operator approach allows for the solving of many computing problems in a more general context of operating spaces. In addition, operator representation of computing devices and their networks allows for the construction of a variety of operator compositions and the development of new schemas of computation as well as network and computer architectures using operations with operators. Besides, operator representation allows for the efficient application of the axiomatic technique for the investigation of computation.

scholarly journals Modeling Computing Devices and Processes by Information Operators

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 18
Author(s):  
Mark Burgin ◽  
Gordana Dodig-Crnkovic
Keyword(s):  
Operator Theory ◽  
Computer Architectures ◽  
General Context ◽  
Theoretical Studies ◽  
Operator Approach ◽  
Operator Representation ◽  
Practical Applications ◽  
Theory Of Computing

The concept of operator is exceedingly important in many areas as a tool of theoretical studies and practical applications. Here, we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, networks, and processes. In particular, the operator approach allows for the solving of many computing problems in a more general context of operating spaces. In addition, operator representation of computing devices and their networks allows for the construction of a variety of operator compositions and the development of new schemas of computation as well as network and computer architectures using operations with operators. Besides, operator representation allows for the efficient application of the axiomatic technique for the investigation of computation.

Mathematical models of Gauss – Kruger projection for calculation of meridians conversion on the plane and scale of the image

2018 ◽  
Vol 934 (4) ◽  
pp. 2-7
Author(s):  
P.A. Medvedev ◽  
M.V. Novgorodskaya
Keyword(s):  
Mathematical Models ◽  
Analytical Methods ◽  
Theoretical Studies ◽  
Spherical Trigonometry ◽  
Cylindrical Projection ◽  
Rectangular Coordinates ◽  
In Series ◽  
Observational Errors ◽  
The Difference

This work contains continued research carried out on improving mathematical models of the Gauss-Krueger projection in accordance with the parameters of any ellipsoid with the removal of points from the axial meridian to l ≤ 6° . In terms of formulae earlier derived by the authors with improved convergence for the calculation of planar rectangular coordinates by geodesic coordinates, the algorithms for determining the convergence of meridians on the plane and the scale of the image are obtained. The improvement of the formulae represented in the form of series in powers of the difference in longitudes was accomplished by separating spherical terms in series and then replacing their approximate sums by exact expressions using the formulae of spherical trigonometry. As in previous works published in this journal [7, 8], determining the sums of the spherical terms was carried out according to the laws of the transverse-cylindrical projection of the sphere on the plane. Theoretical studies are given and formulae are proposed for estimating the observational errors in the results of the derived algorithms. The maximum of observational errors of convergence of meridians and scale, proceeding from the specified accuracy of the determined quantities was established through analytical methods.

scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

scholarly journals Tunable Adhesion of a Bio-Inspired Micropillar Arrayed Surface Actuated by a Magnetic Field

2018 ◽  
Vol 86 (1) ◽  
Author(s):  
Xingji Li ◽  
Zhilong Peng ◽  
Yazheng Yang ◽  
Shaohua Chen
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Magnetic Particles ◽  
Rotation Angle ◽  
Adhesion Force ◽  
Practical Applications ◽  
Section Shape ◽  
Theoretical Predictions ◽  
Large Elastic Deformation ◽  
The Difference

Bio-inspired functional surfaces attract many research interests due to the promising applications. In this paper, tunable adhesion of a bio-inspired micropillar arrayed surface actuated by a magnetic field is investigated theoretically in order to disclose the mechanical mechanism of changeable adhesion and the influencing factors. Each polydimethylsiloxane (PDMS) micropillar reinforced by uniformly distributed magnetic particles is assumed to be a cantilever beam. The beam's large elastic deformation is obtained under an externally magnetic field. Specially, the rotation angle of the pillar's end is predicted, which shows an essential effect on the changeable adhesion of the micropillar arrayed surface. The larger the strength of the applied magnetic field, the larger the rotation angle of the pillar's end will be, yielding a decreasing adhesion force of the micropillar arrayed surface. The difference of adhesion force tuned by the applied magnetic field can be a few orders of magnitude, which leads to controllable adhesion of such a micropillar arrayed surface. Influences of each pillar's cross section shape, size, intervals between neighboring pillars, and the distribution pattern on the adhesion force are further analyzed. The theoretical predictions are qualitatively well consistent with the experimental measurements. The present theoretical results should be helpful not only for the understanding of mechanical mechanism of tunable adhesion of micropillar arrayed surface under a magnetic field but also for further precise and optimal design of such an adhesion-controllable bio-inspired surface in future practical applications.

Machine Learning Analysis and Prediction Models of Alkaline Anion Exchange Membranes for Fuel Cells

2021 ◽  
Author(s):  
Xiuyang Zou ◽  
Ji Pan ◽  
Zhe Sun ◽  
Bowen Wang ◽  
Zhiyu Jin ◽  
...  
Keyword(s):  
Machine Learning ◽  
Fuel Cells ◽  
Anion Exchange ◽  
Prediction Models ◽  
Anion Exchange Membranes ◽  
Theoretical Studies ◽  
Practical Applications ◽  
Alkaline Membrane ◽  
Learning Analysis ◽  
Experimental And Theoretical Studies

The degradation of anion exchange membranes (AEMs) hindered the practical applications of alkaline membrane fuel cells. This issue has inspired a large number of both experimental and theoretical studies. However,...

Formation of transition-metal-based ohmic contacts to n-Mg2Si by Plasma Activated Sintering

2007 ◽  
Vol 1044 ◽  
Author(s):  
Yohei Oguni ◽  
Tsutomu Iida ◽  
Atsunobu Matsumoto ◽  
Takashi Nemoto ◽  
Junichi Onosaka ◽  
...  
Keyword(s):  
Ohmic Contacts ◽  
Thermal Stresses ◽  
Electrode Materials ◽  
Open Circuit ◽  
Activated Sintering ◽  
Practical Applications ◽  
Thermal Expansion Coefficients ◽  
Good Crystalline Quality ◽  
The Difference ◽  
Plasma Activated Sintering

AbstractElectrode materials consisting of Cu, Ti and Ni were formed on Bi-doped n-type Mg2Si by means of a monobloc plasma-activated sintering (PAS) technique. Due to the difference in thermal expansion coefficients between Ti and Mg2Si, rather high residual thermal stresses gave rise to the introduction of cracks, which were mainly located in the Mg2Si layer, when Ti was used as the electrode material. In the case of the Cu electrodes, monobloc sintering could not be performed in a reproducible manner because Cu melts abruptly and effuses at around 973K, which is 100 K lower than the sintering temperature that is required for Mg2Si of good crystalline quality. When compared with the results for Cu and Ti, the monobloc PAS process for Ni was both stable and reproducible. The room-temperature I-V characteristics of Ni electrodes were considered to be adequate for practical applications, with durable Mg2Si-electrode junction properties being realized at a practical operating temperature of 600 K with ΔT = 500 K. The highest open circuit voltage (VOC) observed was 41 mV at ΔT = 500 K (between 873 K and 373 K) for Ni electrodes fabricated using the monobloc PAS process. The voltage (V) and current (I) values with a 10 Ohm load were ∼ 48 mV and ∼ 2 mA at ΔT = 500 K.

scholarly journals On the Quantumness of Multiparameter Estimation Problems for Qubit Systems

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1197
Author(s):  
Sholeh Razavian ◽  
Matteo G. A. Paris ◽  
Marco G. Genoni
Keyword(s):  
Quantum Mechanics ◽  
Statistical Model ◽  
Fundamental Problem ◽  
Practical Applications ◽  
The Matrix ◽  
Estimation Problems ◽  
Estimation Precision ◽  
Quantum Statistical ◽  
The Difference ◽  
Cramer Rao Bound

The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumnessR, a measure that has been recently introduced in order to quantify how incompatible the parameters to be estimated are. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e., the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model, it is equal to the difference between the bounds and, in general, their behavior qualitatively coincide. On the other hand, we also find evidence that, for certain quantum statistical models, the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters.

EXTENDING THE DOUBLY LINKED FACE LIST FOR THE REPRESENTATION OF 2-PSEUDOMANIFOLDS AND 2-MANIFOLDS WITH BOUNDARIES

2011 ◽  
Vol 21 (04) ◽  
pp. 467-494
Author(s):  
THIAGO R. DOS SANTOS ◽  
HANS-PETER MEINZER ◽  
LENA MAIER-HEIN
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Point Of View ◽  
Minimal Amount ◽  
Computer Memory ◽  
Memory Usage ◽  
Surgery Simulation ◽  
Practical Applications ◽  
Software Applications ◽  
Behavioral Observations

The Doubly Linked Face List (DLFL) is a data structure for mesh representation that always ensures topological 2-manifold consistency. Furthermore, it uses a minimal amount of computer memory and allows queries to be performed very efficiently. However, the use of the DLFL for the implementation of practical applications is very limited, mainly because of two drawbacks: (1) the DLFL is only able to represent 2-manifold objects; (2) its operators may be ambiguous, modifying the structure in an unexpected way from the user's point of view. In order to overcome these drawbacks, we present the Extended Doubly Linked Face List (XDLFL), which extends the DLFL for the representation of 2-pseudomanifolds and 2-manifolds with boundaries, increasing its applicability for practical software applications. Using these extensions, we also show how to avoid ambiguities in the original DLFL's operators. A new set of intuitive operators for the manipulation of the extensions and for the unambiguous manipulation of the data structure is also presented. The implementation of these extensions is straightforward, since the modifications to the DLFL are trivial and based on behavioral observations of the DLFL's operators. After integrating the extensions to the DLFL, memory usage increases very slightly, while is still smaller than the memory usage of other well-known data structures. Furthermore, queries related to the new extensions, such as whether an edge belongs to a boundary, may be performed very efficiently. The proposed extensions and their operators are very beneficial for applications such as surgery simulation softwares, where the interactions with the models, such as cutting or appending objects to each other, must be performed in an efficient and transparent manner.

Angle-domain common-image gathers from anisotropic migration

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. S81-S91 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
Complex I ◽  
Theoretical Development ◽  
Isotropic Case ◽  
Data Set ◽  
Practical Applications ◽  
Wavefield Continuation ◽  
The Difference ◽  
Contrast Group ◽  
Vti Media ◽  
The Relationship

I present a general methodology for computing angle-domain common-image gathers (ADCIGs) in conjunction with anisotropic wavefield-continuation migration. The method is based on transforming the prestack image from the subsurface-offset domain to the angle domain using slant stacks. The processing sequence is the same as that for computing ADCIGs for the isotropic case, though the interpretation of the relationship between the slopes measured in the prestack image and the aperture angles is more complex. I demonstrate that the slopes measured by performing slant stacks along the subsurface-offset axis of the prestack image provide a good approximation of the phase aperture angles, and they are exactly equal to the phase aperture angles for flat reflectors in vertical transversly isotropic (VTI) media. In the general case of dipping reflectors, the angles computed using slant stacks can be easily corrected by applying the relationships that I present in this paper, and the accurate aperture angles can be determined as a function of the reflector dip and anisotropic slowness at the reflector. I derive these relationships from both plane-wave and ray viewpoints. This theoretical development links the kinematics in ADCIGs with migration-velocity errors. I apply the proposed method to compute ADCIGs from the prestack image obtained by anisotropic migration of a 2D line recorded in the Gulf of Mexico. I analyze the error introduced by neglecting the difference between the true phase aperture angle and the angle computed through slant stacks, showing that, at least for this data set, these errors are negligible and can be safely ignored. In contrast, group aperture angles can be quite different from phase aperture angles; thus, ignoring the distinction between these two angles can be detrimental to practical applications.

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