Intersection Domain Research Articles

How electrons still guard the space: Electron number distribution functions based on QTAIM∩ELF intersections.

Despite the importance of the one-particle picture provided by the orbital paradigm, a rigorous understanding of the spatial distribution of electrons in molecules is still of paramount importance to chemistry. Considerable progress has been made following the introduction of topological approaches, capable of partitioning space into chemically meaningful regions. They usually provide atomic partitions, for example, through the attraction basins of the electron density in the quantum theory of atoms in molecules (QTAIM) or electron-pair decompositions, as in the case of the electron localization function (ELF). In both cases, the so-called electron distribution functions (EDFs) provide a rich statistical description of the electron distribution in these spatial domains. Here, we take the EDF concept to a new fine-grained limit by calculating EDFs in the QTAIM ∩ ELF intersection domains. As shown in AHn systems based on main group elements, as well as in the CO, NO, and BeO molecules, this approach provides an exquisitely detailed picture of the electron distribution in molecules, allowing for an insightful combination of the distribution of electrons between Lewis entities (such as bonds and lone pairs) and atoms at the same time. Besides mean-field calculations, we also explore the impact of electron correlation through Hartree-Fock (HF), density functional theory (DFT) (B3LYP), and CASSCF calculations.

Adaptive Spatial Complex Fuzzy Inference Systems With Complex Fuzzy Measures

Fuzzy inference systems, in general, and complex fuzzy inference systems, in particular, play an increasingly important role in many fields, such as change detection, image classification, recognition problems, etc. Despite being the well-known technique to solve with time series data, the rulebase still has the considered limitation because of the directly affecting the results as well as the processing time of these methods. To overcome this limitation, this study proposes an Adaptive spatial complex inference system that can automatically infer and adapt to the new remotely sensed image. In the proposed model, to predict the image of time t + 1, the system will generate a new rulebase according to this expected image. This new rulebase and the previous Co-Spatial-CFIS+ rulebase are evaluated using a complex fuzzy measure. This measure is built by determining the intersection domain between two rule spaces; this intersection value estimates removing, merging, or adding a newly generated rule into the current rulebase. Finally, a more suitable set of rules is obtained for image prediction. To illustrate the efficiency of the proposed approach, it is applied to the remote sensing cloud image data of the U.S. Navy. Our model evaluated the model’s effectiveness in comparison to the state-of-the-art along studies in detecting changes in remote sensing cloud images. Moreover, the findings of the experiments revealed that the proposed model could improve the change detection results in terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , RMSE, time-consuming, and the number of rules.

Filosofické problémy nanotechnologií: ontologicko-systémová východiska a etické implikace

From the perspective of philosophy of science and technologies, we firstly attend to the issue of the role of nanotechnologies within the evolution of technologies. We recognize their utmost importance in the respect that they are technologies of life itself. We further explain that the nano-level is the domain of intersection of the rules of quantum physics and traditional Newtonian physics. This is our starting point from which we discuss the issue of conditions under which minimizing things also changes their functional essence. We use the example of the Drexler vs. Smalley debate to demonstrate the paradigmatic incomparability of the two perspectives and the physical-chemical and engineering-related limits of nanotechnologies. We discuss to what extent are the dangers and ethical implications emerging from Drexler’s contemplations real, be it what he calls the “grey goo” problem or the issues of molecular production. We regard certain problems linked to synthetic biology as more serious. We conclude our text with the consideration that the human civilization should think of the possibilities of nanotechnologies in the development of life as an existential challenge.

Trajectory surface hopping vs. quantum scattering calculations on D+ + H2 and H + [formula omitted] reactions using ab initio surfaces and couplings

We employ trajectory surface hopping (TSH) formalism [Chem. Phys. 349 (2008) 334, J. Chem. Phys. 142 (2015) 144307] to compute cross-sections or/and rate constants of D+ + H2 (v=0,j=0) and H + H2+ (v=0,j=0) reactions initiating from ground and first excited electronic state of H3+, respectively. While solving Hamilton’s equations over adiabatic potential energy surfaces (PESs), switching probabilities are calculated by ab initio nonadiabatic coupling terms for the first time. During hopping, momenta are adjusted to fulfil total energy conservation, where a scaling factor is introduced to explore the conservation of linear momentum. For non-charge transfer process, quasi-classical cross-sections match well with quantum results obtained from diabatic PESs of H3+ and experimental findings, but deviations are observed at the energy domain of conical intersection driven hopping for charge-transfer processes. Calculated results indicate the origin of limitations of TSH algorithm as well as depict computational advantage with respect to quantum dynamics.

Lens mediated scattering of sound by sound with finite aperture beams.

An experimental concept for measuring sound-sound scattering of finite aperture acoustic beams in a water tank facility is presented. In order to achieve a measurable effect, the beams are collimated within their intersection domain by a focusing acoustic lens. A paraxial quasi-linear split step simulation tool has been developed and used in order to determine and optimize experiment setup parameters. The scattered part of the difference frequency field was measured and found to be compatible with simulations. Furthermore, the primary beams were also monitored in order to guarantee full compatibility with simulated propagation and compare the measured difference field with the overlap contribution. A spatially coherent post processing filtering was applied in order to improve the signal to noise ratio. A distinct clear scattering peak in the difference field has been identified propagating with the predicted off axis tilt angle.

Формирование признакового пространства периодических временных зависимостей для систем диагностики состояния динамических объектов на примере сетчатки глаза

The technology of testing dynamically and structurally similar aircraft models for flutter in subsonic wind tunnels using information and The article addresses techniques for setting up the attribute space of informative features of periodic signals recorded at the output of a dynamic object with an unknown structure in response to rectangular testing signals of different frequencies applied to the object input. The attribute space is used in developing expert systems for diagnosing the current state of an operating dynamic object. With a great variety of possible developing faults, the simplest practical techniques involving the use of characteristic points of change in the observed time dependencies yield a limited number of features with large mutual intersection domains. To expand the attribute space, it is proposed to use the expansion of input and output signals into a Fourier series for setting up a base of additional features. The proposed features characterize, depending on the testing conditions, the object’s transferring properties in the frequency domain from changes in its amplitude and phase characteristics. The test pulse frequency and duration serve as such conditions. For the convenience of comparing the object’s frequency responses variation pattern, two special procedures are used. The first procedure allows the observed time dependencies to be reduced to a single pseudo frequency of the test signals. The second procedure uses specially formed windows for subjecting individual fragments of the observed time dependencies to a spectral analysis. It is shown that, depending on the type of the frequency responses being analyzed, the techniques for their polynomial approximation, as well as integral estimates of frequency response individual domains can be useful. The polynomial approximation makes it possible to use the coefficients of the approximating polynomials as additional features, and the integration of individual characteristic domains of the frequency responses makes it possible to introduce dimensionless relative indicators that characterize the degree of change in the frequency responses depending on the experimental conditions. The considered techniques open the possibility to select additional features that can help distinguish both separate groups of faults and individual faults in operating objects. The study results are illustrated by the examples of analyzing the changes in electroretinograms that record changes in the eye retina biopotential in response to light flashes of different frequencies.

Eliminating the end effect of empirical mode decomposition using a cubic spline based method

The empirical mode decomposition (EMD) is a method that is commonly applied to extract the intrinsic mode functions (IMFs) of a signal by a sifting process, which requires imposing the extended extrema at both ends of the signal (i.e., the end condition). The imposition of extended extrema can cause an error, which is often presented by the changing shapes of original envelopes and distort extracted IMFs, which is described as the end effect. An important issue during the application of the EMD is restricting the end effect. This paper reveals the decisive factors that can restrict the end effect by determining the uniqueness of the envelope, and provides an interpretation of the end effect in terms of the differences between the original envelope and the extended envelope based on the cubic spline theory. Two principles that are important to the design of an end condition method are provided. The first principle is that the domain of the extended envelope needs to cover the original signal; the second is that the ordinate value of the extended local maxima is greater than or equal to that of the extended local minima. Following these two principles, a new end condition method, the cubic spline based method (CSBM), is proposed in this study. The novelty of the CSBM is that the extended envelope maintains the shape of the original envelope in their intersection domain, and the end effect can be restricted in a limited domain during the sifting process of EMD for each different input signal. Six signals are used to demonstrate the performance of the CSBM by comparing them with two other end condition methods, the extreme method and the improved slope based method (ISBM). The six signals include: a damped sinusoid signal, four monovariate signals with various amplitude modulation-frequency modulation (AM-FM) behaviors, and a one-channel functional near-infrared spectroscopy (fNIRS) signal. Results show that the CSBM in general performs better than the other two methods.

Maximal Cohen–Macaulay tensor products

In this paper, we are concerned with the following question: if the tensor product of finitely generated modules M and N over a local complete intersection domain is maximal Cohen–Macaulay, then must M or N be a maximal Cohen–Macaulay? Celebrated results of Auslander, Lichtenbaum, and Huneke and Wiegand yield affirmative answers to the question when the ring considered has codimension zero or one, but the question is very much open for complete intersection domains that have codimension at least two, even open for those that are one-dimensional, or isolated singularities. Our argument exploits Tor-rigidity and proves the following, which seems to give a new perspective to the aforementioned question: if R is a complete intersection ring which is an isolated singularity such that $$\dim (R)>{{\,\mathrm{codim}\,}}(R)$$ , and the tensor product $$M\otimes _RN$$ is maximal Cohen–Macaulay, then M is maximal Cohen–Macaulay if and only if N is maximal Cohen–Macaulay.

Point-by-point prediction of cutting force in 3-axis CNC milling machines through voxel framework in digital manufacturing

A new digital-based model is presented for the prediction of cutting forces in 3-axis CNC milling of surfaces. The model uses an algorithm to detect the work-piece/cutter intersection domain automatically for given cutter location, cutter and work-piece geometries. The algorithm uses a voxel-based representation for the workpiece and rasterized tool slice to detect the tool engagement. Furthermore, an analytical approach is used to calculate the cutting forces based on the discretized model. The results of model validation experiments on machining PMMA, Aluminum 6061 and 304 Stainless Steel are presented. Comparisons of the predicted and measured forces show that this digital approach can be used to accurately predict forces during machining.

Optimization of Deployment Quality for Intrusion Detection in Surveillance Wireless Sensor Network

The volatile nature of wireless sensor network promise a lot of scopes in diverse disciplines. It is highly applicable in hostile environment, where nodes can be only deployed randomly, without having any predetermined statistical distribution. The fundamental challenges arise to provide maximum coverage and connectivity in hostile vicinity. A detailed analysis of node density, is required to achieve appropriate coverage. The problem of coverage is solved by optimum distribution scenario and sensing range of sensor nodes. Our goal is to achieve promising deployment quality and detection probability, by mapping the problem of intruder detection with geometric intersection domain, a tool from integral geometry and geometric probability. The proposed deployment quality analysis computes number of sensor nodes, required to attain optimum detection performance.

Grothendieck–Lefschetz theorem with base locus

We compute the divisor class group of the general hypersurface Y of a complex projective normal variety X of dimension at least four containing a fixed base locus Z. We deduce that completions of normal local complete intersection domains of finite type over C of dimension ≥ 4 are completions of UFDs of finite type over C.

Torsion in tensor powers of modules

AbstractTensor products usually have nonzero torsion. This is a central theme of Auslander's 1961 paper; the theme continues in the work of Huneke and Wiegand in the 1990s. The main focus in this article is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modules N with the property that M ⊗R N has nonzero torsion unless M is very special. An important example of such a module N is the Frobenius power peR over a complete intersection domain R of characteristic p &gt; 0.

Prediction of Cutting Force in 3-Axis CNC Milling Machines Based on Voxelization Framework for Digital Manufacturing

A new digital-based model is presented for the prediction cutting forces in 3-axis CNC milling of surfaces. The model uses an algorithm to detect the work-piece/cutter intersection domain automatically for given cutter location (CL), cutter and work-piece geometries. The algorithm uses a voxelization framework to voxelize the cutter helix as well as the work-piece and based on voxel intersections between them can detect the tool engagement. Furthermore, an analytical approach is used to calculate the cutting forces based on the discretized model. The results of model validation experiments on machining PMMA and Aluminum 6061 are also reported. Comparisons of the predicted and measured forces show that this digital approach can be used to accurately predict forces during machining.

Ideals generated by principal minors

A minor is principal means it is defined by the same row and column indices. We study ideals generated by principal minors of size $t\leq n$ of a generic $n\times n$ matrix $X$, in the polynomial ring generated over an algebraically closed field by the entries of $X$. When $t=2$ the resulting quotient ring is a normal complete intersection domain. We show for any $t$, upon inverting $\det X$ the ideals given respectively by the size $t$ and the size $n-t$ principal minors become isomorphic. From that we show the algebraic set given by the size $n-1$ principal minors has a codimension $4$ component defined by the determinantal ideal, plus a codimension $n$ component. When $n=4$ the two components are linked, and in fact, geometrically linked.

Excellent normal local domains and extensions of Krull domains

We consider properties of extensions of Krull domains such as flatness that involve behavior of extensions and contractions of prime ideals. Let (R,m) be an excellent normal local domain with field of fractions K, let y be a nonzero element of m and let R⁎ denote the (y)-adic completion of R. For elements τ1,…,τs of yR⁎ that are algebraically independent over R, we construct two associated Krull domains: an intersection domain A:=K(τ1,…τs)∩R⁎ and its approximation domain B; see Setting 2.2.If in addition R is countable with dimR≥2, we prove that there exist elements τ1,…,τs,… as above such that, for each s∈N, the extension R[τ1,…,τs]↪R⁎[1/y] is flat; equivalently, B=A and A is Noetherian. Using this result we establish the existence of a normal Noetherian local domain B such that: B dominates R; B has (y)-adic completion R⁎; and B contains a height-one prime ideal p such that R⁎/pR⁎ is not reduced. Thus B is not a Nagata domain and hence is not excellent.We present several theorems involving the construction. These theorems yield examples where B⊊A and A is Noetherian while B is not Noetherian; and other examples where B=A and A is not Noetherian.

Self-Localization at Street Intersections.

There is growing interest among smartphone users in the ability to determine their precise location in their environment for a variety of applications related to wayfinding, travel and shopping. While GPS provides valuable self-localization estimates, its accuracy is limited to approximately 10 meters in most urban locations. This paper focuses on the self-localization needs of blind or visually impaired travelers, who are faced with the challenge of negotiating street intersections. These travelers need more precise self-localization to help them align themselves properly to crosswalks, signal lights and other features such as walk light pushbuttons. We demonstrate a novel computer vision-based localization approach that is tailored to the street intersection domain. Unlike most work on computer vision-based localization techniques, which typically assume the presence of detailed, high-quality 3D models of urban environments, our technique harnesses the availability of simple, ubiquitous satellite imagery (e.g., Google Maps) to create simple maps of each intersection. Not only does this technique scale naturally to the great majority of street intersections in urban areas, but it has the added advantage of incorporating the specific metric information that blind or visually impaired travelers need, namely, the locations of intersection features such as crosswalks. Key to our approach is the integration of IMU (inertial measurement unit) information with geometric information obtained from image panorama stitchings. Finally, we evaluate the localization performance of our algorithm on a dataset of intersection panoramas, demonstrating the feasibility of our approach.

Are complete intersections complete intersections?

A commutative local ring is generally defined to be a complete intersection if its completion is isomorphic to the quotient of a regular local ring by an ideal generated by a regular sequence. It has not previously been determined whether or not such a ring is necessarily itself the quotient of a regular ring by an ideal generated by a regular sequence. In this article, it is shown that if a complete intersection is a one dimensional integral domain, then it is such a quotient. However, an example is produced of a three dimensional complete intersection domain which is not a homomorphic image of a regular local ring, and so the property does not hold in general.

Exploring fabrication tolerances of optical systems by solving inequalities

A scheme to study fabrication tolerances of optical components and systems is presented. By solving a set of non-linear inequalities an optimal set of lens parameters is found. Then, by selecting another, but strict, set of boundaries to the non-linear inequalities system, a new set of lens parameters is found. The fabrication tolerances are determined by the intersection domain of each lens parameters obtained by solving the set of non-linear equations, with a condition that one solution should come from a strict set on boundaries of the non-linear equation system. This scheme is applied to a classical triplet lens system, used as starting point, and is compacted in effective and back focuses lengths, showing the versatility to study the fabrication tolerances.

Comments on I1-branes

We explore the supergravity solution of D5-branes intersecting as an I1-brane. In a suitable near-horizon limit the geometry is in qualitative agreement with that found in the microscopic open-string analysis as well as the NS5-brane analysis of Itzhaki, Kutasov and Seiberg. In particular, the ISO(1,1) Lorentz symmetry of the intersection domain is enhanced to ISO(1,2). The discussion is generalised to the T-dual configuration of a D4-brane intersecting a D6-brane. In this case the ISO(1,1) symmetry is not enhanced. This is true both in the supergravity approximation to the weakly coupled string theory and to the M-theory limit.

An Enhanced Force Model for Sculptured Surface Machining

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.