Journal articles: 'Almost orthogonality'

1

Kopecká, Eva. "Almost isometries and orthogonality." Journal of Functional Analysis 222, no. 2 (May 2005): 253–73. http://dx.doi.org/10.1016/j.jfa.2005.01.006.

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Chmieliński, Jacek, and Jürg Rätz. "Orthogonality equation almost everywhere." Publicationes Mathematicae Debrecen 52, no. 3-4 (April 1, 1998): 317–35. http://dx.doi.org/10.5486/pmd.1998.2008.

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Torres, Rodolfo H. "Almost-Orthogonality in Fourier Analysis." Notices of the American Mathematical Society 67, no. 08 (September 1, 2020): 1. http://dx.doi.org/10.1090/noti2133.

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4

Minkin, Arcady. "Almost orthogonality of Birkhoff’s Solutions." Results in Mathematics 24, no. 3-4 (November 1993): 280–87. http://dx.doi.org/10.1007/bf03322336.

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Ben-Yaacov, Itay, and Frank O. Wagner. "On almost orthogonality in simple theories." Journal of Symbolic Logic 69, no. 2 (June 2004): 398–408. http://dx.doi.org/10.2178/jsl/1082418533.

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Abstract.1. We show that if p is a real type which is internal in a set Σ of partial types in a simple theory, then there is a type p′ interbounded with p, which is finitely generated over Σ, and possesses a fundamental system of solutions relative to Σ.2. If p is a possibly hyperimaginary Lascar strong type, almost Σ-internal, but almost orthogonal to Σω, then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts on p while fixing Σ generically In case p is Σ-internal and T is stable, this is the binding group of p over Σ.

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Weigt, Julian. "Almost-orthogonality of restricted Haar functions." Proceedings of the American Mathematical Society 148, no. 2 (October 18, 2019): 601–9. http://dx.doi.org/10.1090/proc/14752.

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Shirshova, Elen E. "On groups with the almost orthogonality condition." Communications in Algebra 28, no. 10 (January 2000): 4803–18. http://dx.doi.org/10.1080/00927870008827121.

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He, Chan, and Dan Wang. "A Remark on the Homogeneity of Isosceles Orthogonality." Journal of Function Spaces 2014 (2014): 1–3. http://dx.doi.org/10.1155/2014/876015.

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Inspired by the definition of homogeneous direction of isosceles orthogonality, we introduce the notion of almost homogeneous direction of isosceles orthogonality and show that, surprisingly, these two notions coincide. Several known characterizations of inner products are improved.

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Bényi, Árpád, and Rodolfo H. Torres. "Almost orthogonality and a class of bounded bilinear pseudodifferential operators." Mathematical Research Letters 11, no. 1 (2004): 1–11. http://dx.doi.org/10.4310/mrl.2004.v11.n1.a1.

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Liao, Fanghui, and Zongguang Liu. "Some Properties of Triebel–Lizorkin and Besov Spaces Associated with Zygmund Dilations." Canadian Mathematical Bulletin 59, no. 4 (December 1, 2016): 834–48. http://dx.doi.org/10.4153/cmb-2016-030-9.

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AbstractIn this paper, using Calderón’s reproducing formula and almost orthogonality estimates, we prove the lifting property and the embedding theorem of the Triebel–Lizorkin and Besov spaces associated with Zygmund dilations.

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Carbery, Anthony. "An almost-orthogonality principle with applications to maximal functions associated to convex bodies." Bulletin of the American Mathematical Society 14, no. 2 (April 1, 1986): 269–74. http://dx.doi.org/10.1090/s0273-0979-1986-15436-4.

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Paseka, Jan, Wu Junde, and Lei Qiang. "Almost Orthogonality and Hausdorff Interval Topologies of de Morgan Lattices and Lattice Effect Algebras." International Journal of Theoretical Physics 52, no. 6 (January 9, 2013): 2055–64. http://dx.doi.org/10.1007/s10773-012-1465-3.

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Rofallski, Robin, and Thomas Luhmann. "An Efficient Solution to Ray Tracing Problems in Multimedia Photogrammetry for Flat Refractive Interfaces." PFG – Journal of Photogrammetry, Remote Sensing and Geoinformation Science 90, no. 1 (March 2022): 37–54. http://dx.doi.org/10.1007/s41064-022-00192-1.

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AbstractUnderstanding and considering refraction effects are important parts of the demanding task of multimedia photogrammetry, especially with planar interfaces, so-called ”flat ports”. Yet, it remains challenging to determine reliable calibration results that are both quickly acquired and physically interpretable. In this contribution, a novel object-based optimization algorithm, relying on ray tracing methods, is introduced. It enables calibrating physical parameters of all involved refractive properties with reduced computational effort, compared to other standard algorithms in ray tracing. We show that this solution produces equally accurate results as other ray tracing approaches while improving processing speed by a factor of approximately ten and providing a statistical metric in object space. Furthermore, we show in a laboratory investigation that explicit calibration of refractive properties is crucial even with orthogonally aligned bundle-invariant interfaces for highest accuracy, as accuracy in object space is decreased by about 10% with implicit calibration. With deviation from orthogonality by about ten degrees this decreases even further to almost no useful results and accuracy loss of more than 50% compared to explicit calibration results.

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Chiang, Yik-Man, and Guo-Fu Yu. "Galoisian approach to complex oscillation theory of some Hill equations." MATHEMATICA SCANDINAVICA 124, no. 1 (January 13, 2019): 102–31. http://dx.doi.org/10.7146/math.scand.a-110889.

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We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponent of convergence of zeros) of certain Hill equations considered by Bank and Laine using Nevanlinna theory must be Liouvillian solutions. These are solutions obtainable by suitable differential field extension constructions. In particular, we establish a full correspondence between solutions of non-oscillatory type and Liouvillian solutions for a particular Hill equation. Explicit closed-form solutions are obtained via both methods for this Hill equation whose potential is a combination of four exponential functions in the Bank-Laine theory. The differential equation is a periodic form of a biconfluent Heun equation. We further show that these Liouvillian solutions exhibit novel single and double orthogonality, and satisfy Fredholm integral equations over suitable integration regions in $\mathbb{C}$ that mimic single/double orthogonality for the corresponding Liouvillian solutions of the Lamé and Whittaker-Hill equations, discovered by Whittaker and Ince almost a century ago.

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15

Sweezy, Caroline. "An extension of a norm inequality for a semi-discrete g*λ function." Applicable Analysis and Discrete Mathematics 3, no. 2 (2009): 177–97. http://dx.doi.org/10.2298/aadm0902177s.

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A norm inequality for a semi-discrete g*?(f) function is obtained for functions, f, that can be written as a sum whose terms consist of a numerical coefficient multiplying a member of a family of functions that have properties of geometric decay, minimal smoothness and almost orthogonality condition. The theorem is applied to the rate of change of u, a solution to Lu = div?f in a bounded, nonsmooth domain ? Rd, d?3, u = 0 on ??.

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ANDRECUT, M., and M. K. ALI. "ON THE ADIABATIC QUANTUM EVOLUTION OF A SINGLE QUBIT." International Journal of Quantum Information 02, no. 04 (December 2004): 447–52. http://dx.doi.org/10.1142/s0219749904000432.

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The adiabatic quantum evolution method has generally been studied for the case where the linear interpolation from an initial to a final Hamiltonian is taken. However, this approach fails even for the case of a single qubit, when the initial and final states are orthogonal or almost orthogonal. In this case, the evolution time becomes infinite. We show that by using a simple nonlinear interpolation method the adiabatic evolution can be done in finite time, regardless of the orthogonality of the initial and final states.

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17

Westheimer, G., and W. Li. "Classifying illusory contours by means of orientation discrimination." Journal of Neurophysiology 75, no. 2 (February 1, 1996): 523–37. http://dx.doi.org/10.1152/jn.1996.75.2.523.

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1. Thresholds for discrimination of orientation were measured for solid and interrupted lines, and for illusory borders defined by offset abutting lines of a variety of configurations. 2. Illusory contours defined by orthogonal lines with a clear gap or overlap manifest excellent orientation discrimination even for very short exposure durations, and are robust to pattern motion and masking. The performance is almost as good as that for real lines. 3. When the contour is made up of abutting lines without gap or overlap, orientation discrimination is not nearly as good, and deteriorates further with short exposure duration, with target motion, and with masking. 4. The introduction of disparity in such illusory borders does not improve the discrimination of its orientation, so that concepts such as surface elaborations do not yet have to be invoked. 5. The results suggest that there is one class of illusory contour whose orientations can be discriminated by virtue of its delivering adequate stimuli to orientation-selective units in primary visual cortex. For contours with a uniform space-averaged luminance, the orientation discrimination is helped by the orthogonality of the generating lines, and this gives support to the concept that orthogonally oriented end-stopped neurons may participate in the orientation discrimination.

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ALFONSECA, ANGELES. "STRONG TYPE INEQUALITIES AND AN ALMOST-ORTHOGONALITY PRINCIPLE FOR FAMILIES OF MAXIMAL OPERATORS ALONG DIRECTIONS IN ${\bb R}^2$." Journal of the London Mathematical Society 67, no. 01 (February 2003): 208–18. http://dx.doi.org/10.1112/s0024610702003915.

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19

Currey, Bradley N. "Admissibility for a Class of Quasiregular Representations." Canadian Journal of Mathematics 59, no. 5 (October 1, 2007): 917–42. http://dx.doi.org/10.4153/cjm-2007-039-0.

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AbstractGiven a semidirect product G = N ⋊ H where N is nilpotent, connected, simply connected and normal in G and where H is a vector group for which ad() is completely reducible and R-split, let τ denote the quasiregular representation of G in L2(N). An element ψ ∈ L2(N) is said to be admissible if the wavelet transform f ⟼ 〈 f, τ(·)ψ 〉 defines an isometry from L2(N) into L2(G). In this paper we give an explicit construction of admissible vectors in the case where G is not unimodular and the stabilizers in H of its action on are almost everywhere trivial. In this situation we prove orthogonality relations and we construct an explicit decomposition of L2(G) into G-invariant, multiplicity-free subspaces each of which is the image of a wavelet transform . We also show that, with the assumption of (almost-everywhere) trivial stabilizers, non-unimodularity is necessary for the existence of admissible vectors.

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Garanzha, Vladimir A., Lyudmila N. Kudryavtseva, and Aleksei I. Belokrys-Fedotov. "Single and multiple springback technique for construction and control of thick prismatic mesh layers." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 1 (February 1, 2021): 1–15. http://dx.doi.org/10.1515/rnam-2021-0001.

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Abstract We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices of the surface mesh we use quadratic programming algorithm based on the nearest ball concept. This pre-stressed material expands, possibly with self-penetration and extrusion to exterior of computational domain until target layer thickness is attained. Special preconditioned relaxation procedure is proposed based on the solution of stationary springback problem. It is shown that preconditioner can handle very stiff problems. Once an offset prismatic mesh is constructed, self-intersections are eliminated using iterative prism cutting procedure.Next, variational advancing front procedure is applied for refinement and precise orthogonalization of prismatic layer near boundaries. We demonstrate that resulting mesh layer is ‘almost mesh-independent’ in a sense that the dependence of thickness and shape of the layer on mesh resolution and triangle quality is weak. It is possible to apply elastic springback technique sequentially layer by layer. We compare single springback technique with multiple springback technique in terms of mesh quality, stiffness of local variational problems and mesh orthogonality or/and layer thickness balance.

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Ivers, D. J., A. Jackson, and D. Winch. "Enumeration, orthogonality and completeness of the incompressible Coriolis modes in a sphere." Journal of Fluid Mechanics 766 (February 4, 2015): 468–98. http://dx.doi.org/10.1017/jfm.2015.27.

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AbstractWe consider incompressible flows in the rapid-rotation limit of small Rossby number and vanishing Ekman number, in a bounded volume with a rigid impenetrable rotating boundary. Physically the flows are inviscid, almost rigid rotations. We interpret the Coriolis force, modified by a pressure gradient, as a linear operator acting on smooth inviscid incompressible flows in the volume. The eigenfunctions of the Coriolis operator $\boldsymbol{{\mathcal{C}}}$ so defined are the inertial modes (including any Rossby modes) and geostrophic modes of the rotating volume. We show $\boldsymbol{{\mathcal{C}}}$ is a bounded operator and that $-\text{i}\boldsymbol{{\mathcal{C}}}$ is symmetric, so that the Coriolis modes of different frequencies are orthogonal. We prove that the space of incompressible polynomial flows of degree $N$ or less in a sphere is invariant under $\boldsymbol{{\mathcal{C}}}$. The symmetry of $-\text{i}\boldsymbol{{\mathcal{C}}}$ thus implies the Coriolis operator is non-defective on the finite-dimensional space of spherical polynomial flows. This enables us to enumerate the Coriolis modes, and to establish their completeness using the Weierstrass polynomial approximation theorem. The fundamental tool, which is required to establish invariance of spherical polynomial flows under $\boldsymbol{{\mathcal{C}}}$ and completeness, is that the solution of the polynomial Poisson–Neumann problem, i.e. Poisson’s equation with a Neumann boundary condition and polynomial data, in a sphere is a polynomial. We also enumerate the Coriolis modes in a sphere, with careful consideration of the geostrophic modes, directly from the known analytic solutions.

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Bruschi, M., F. Calogero, and R. Droghei. "Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme." Advances in Mathematical Physics 2009 (2009): 1–43. http://dx.doi.org/10.1155/2009/268134.

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In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros—generally given by simple expressions in terms ofintegers(Diophantinerelations). The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold. Most of these results are not (yet) reported in the standard compilations.

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Vakhania, N. "Orthogonal Random Vectors and the Hurwitz-Radon-Eckmann Theorem." gmj 1, no. 1 (February 1994): 99–113. http://dx.doi.org/10.1515/gmj.1994.99.

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Abstract In several different aspects of algebra and topology the following problem is of interest: find the maximal number of unitary antisymmetric operators Ui in with the property UiUj = –UjUi (i ≠ j). The solution of this problem is given by the Hurwitz-Radon-Eckmann formula. We generalize this formula in two directions: all the operators Ui must commute with a given arbitrary self-adjoint operator and H can be infinite-dimensional. Our second main result deals with the conditions for almost sure orthogonality of two random vectors taking values in a finite or infinite-dimensional Hilbert space H. Finally, both results are used to get the formula for the maximal number of pairwise almost surely orthogonal random vectors in H with the same covariance operator and each pair having a linear support in H ⊕ H. The paper is based on the results obtained jointly with N.P.Kandelaki (see [Vakhania and Kandelaki, Dokl. Akad. Nauk SSSR 294: 528-531, 1987, Dokl. Akad. Nauk SSSR 296: 265-266, 1988, Trudy Inst. Vychisl. Mat. Akad. Nauk Gruz. SSR 28: 11-37, 1988]).

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Santos-Moreno, Javier, and Yolanda Schaerli. "CRISPR-based gene expression control for synthetic gene circuits." Biochemical Society Transactions 48, no. 5 (September 23, 2020): 1979–93. http://dx.doi.org/10.1042/bst20200020.

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Synthetic gene circuits allow us to govern cell behavior in a programmable manner, which is central to almost any application aiming to harness engineered living cells for user-defined tasks. Transcription factors (TFs) constitute the ‘classic’ tool for synthetic circuit construction but some of their inherent constraints, such as insufficient modularity, orthogonality and programmability, limit progress in such forward-engineering endeavors. Here we review how CRISPR (clustered regularly interspaced short palindromic repeats) technology offers new and powerful possibilities for synthetic circuit design. CRISPR systems offer superior characteristics over TFs in many aspects relevant to a modular, predictable and standardized circuit design. Thus, the choice of CRISPR technology as a framework for synthetic circuit design constitutes a valid alternative to complement or replace TFs in synthetic circuits and promises the realization of more ambitious designs.

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Yin, Zhendong, Zhirui Wang, Xiaohui Liu, and Zhilu Wu. "Design of Pulse Waveform for Waveform Division Multiple Access UWB Wireless Communication System." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/171875.

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A new multiple access scheme, Waveform Division Multiple Access (WDMA) based on the orthogonal wavelet function, is presented. After studying the correlation properties of different categories of single wavelet functions, the one with the best correlation property will be chosen as the foundation for combined waveform. In the communication system, each user is assigned to different combined orthogonal waveform. Demonstrated by simulation, combined waveform is more suitable than single wavelet function to be a communication medium in WDMA system. Due to the excellent orthogonality, the bit error rate (BER) of multiuser with combined waveforms is so close to that of single user in a synchronous system. That is to say, the multiple access interference (MAI) is almost eliminated. Furthermore, even in an asynchronous system without multiuser detection after matched filters, the result is still pretty ideal and satisfactory by using the third combination mode that will be mentioned in the study.

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Srivastava, Hari M., Firdous A. Shah, and Waseem Z. Lone. "Quadratic-Phase Wave-Packet Transform in L2(ℝ)." Symmetry 14, no. 10 (September 26, 2022): 2018. http://dx.doi.org/10.3390/sym14102018.

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Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be inadequate for representing those signals whose energy is not well concentrated in the frequency domain. In pursuit of representations of such signals, we propose a novel time-frequency transform coined as quadratic-phase wave packet transform in L2(R). The proposed transform is aimed at rectifying the conventional wavelet transform by employing a quadratic-phase Fourier transform with extra degrees of freedom. Besides the formulation of all the fundamental results, including the orthogonality relation, reconstruction formula and the characterization of range, we also derive a direct relationship between the well-known Wigner-Ville distribution and the proposed transform. In addition, we study the quadratic-phase wave-packet transform in the framework of almost periodic functions. Finally, we extend the scope of the present work by investigating the composition of quadratic-phase wave packet transforms.

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Figgis, BN, and PA Reynolds. "An Xα ab initio Calculation of the Charge and Spin-Density in Cs3Mo(NCS)6 Crystals Compared With Experiment." Australian Journal of Chemistry 43, no. 6 (1990): 1097. http://dx.doi.org/10.1071/ch9901097.

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We have performed ab initio discrete variational Xα calculations on a Cs18[Mo(NCS)6]15+ cluster, with the external electric field appropriate for a Cs3Mo(NCS)6 crystal. The calculations show both σ and π bonding, and also the participation of diffuse molybdenum- centred orbitals . Compared with the charge density experiment these effects are qualitatively correct but are underestimated. We performed further calculations successively removing the external electric field and the 18 Cs+ neighbours . The effects on the calculated metal- ligand bonding in the complex ion are negligible. This is not in agreement with experiment, so that these calculations which invoke only electrostatic effects and orthogonality with neighbouring ions and which also use only simple basis sets are not adequate. Further calculations on the Cr(NCS)63- and W(NCS)63- ions show increasing covalence from chromium to tungsten as expected. The spin transfer to the ligand is calculated to triple, but charge transfer is almost constant.

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He, Shaoyong, and Jiecheng Chen. "Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type." Forum Mathematicum 34, no. 1 (December 1, 2021): 175–96. http://dx.doi.org/10.1515/forum-2021-0204.

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Abstract The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of general product singular integral operators introduced by Han, Li and Lin [Y. Han, J. Li and C.-C. Lin, Criterion of the L 2 L^{2} boundedness and sharp endpoint estimates for singular integral operators on product spaces of homogeneous type, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 2016, 3, 845–907] on the multiparameter Lipschitz spaces of homogeneous type M ~ = M 1 × ⋯ × M n {\tilde{M}=M_{1}\times\cdots\times M_{n}} . Each factor space M i {M_{i}} , 1 ≤ i ≤ n {1\leq i\leq n} , is a space of homogeneous type in the sense of Coifman and Weiss. These operators generalize those studied by Journé on the Euclidean space and include operators studied by Nagel and Stein on Carnot–Carathéodory spaces. The main tool used here is the discrete Littlewood–Paley–Stein theory and almost orthogonality together with a density argument for the product Lipschitz spaces in the weak sense.

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Carini, Alberto, Stefania Cecchi, and Simone Orcioni. "Robust Room Impulse Response Measurement Using Perfect Periodic Sequences for Wiener Nonlinear Filters." Electronics 9, no. 11 (October 29, 2020): 1793. http://dx.doi.org/10.3390/electronics9111793.

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The paper discusses a measurement approach for the room impulse response (RIR), which is insensitive to the nonlinearities that affect the measurement instruments. The approach employs as measurement signals the perfect periodic sequences for Wiener nonlinear (WN) filters. Perfect periodic sequences (PPSs) are periodic sequences that guarantee the perfect orthogonality of a filter basis functions over a period. The PPSs for WN filters are appealing for RIR measurement, since their sample distribution is almost Gaussian and provides a low excitation to the highest amplitudes. RIR measurement using PPSs for WN filters is studied and its advantages and limitations are discussed. The derivation of PPSs for WN filters suitable for RIR measurement is detailed. Limitations in the identification given by the underestimation of RIR memory, order of nonlinearity, and effect of measurement noise are analysed and estimated. Finally, experimental results, which involve both simulations using signals affected by real nonlinear devices and real RIR measurements in the presence of nonlinearities, compare the proposed approach with the ones that are based on PPSs for Legendre nonlinear filter, maximal length sequences, and exponential sweeps.

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SAITO, HIROKI, and HITOSHI TANAKA. "DIRECTIONAL MAXIMAL OPERATORS AND RADIAL WEIGHTS ON THE PLANE." Bulletin of the Australian Mathematical Society 89, no. 3 (September 12, 2013): 397–414. http://dx.doi.org/10.1017/s0004972713000804.

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AbstractLet $\Omega $ be the set of unit vectors and $w$ be a radial weight on the plane. We consider the weighted directional maximal operator defined by $$\begin{eqnarray*}{M}_{\Omega , w} f(x): = \sup _{x\in R\in \mathcal{B} _{\Omega }}\frac{1}{w(R)} \int \nolimits \nolimits_{R} \vert f(y)\vert w(y)\hspace{0.167em} dy,\end{eqnarray*}$$ where ${ \mathcal{B} }_{\Omega } $ denotes the set of all rectangles on the plane whose longest side is parallel to some unit vector in $\Omega $ and $w(R)$ denotes $\int \nolimits \nolimits_{R} w$. In this paper we prove an almost-orthogonality principle for this maximal operator under certain conditions on the weight. The condition allows us to get the weighted norm inequality $$\begin{eqnarray*}\Vert {M}_{\Omega , w} f\mathop{\Vert }\nolimits_{{L}^{2} (w)} \leq C\log N\Vert f\mathop{\Vert }\nolimits_{{L}^{2} (w)} ,\end{eqnarray*}$$ when $w(x)= \vert x\hspace{-1.2pt}\mathop{\vert }\nolimits ^{a} $, $a\gt 0$, and when $\Omega $ is the set of unit vectors on the plane with cardinality $N$ sufficiently large.

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Hwu, C. "Stroh-Like Complex Variable Formalism for the Bending Theory of Anisotropic Plates." Journal of Applied Mechanics 70, no. 5 (September 1, 2003): 696–707. http://dx.doi.org/10.1115/1.1600474.

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Based upon the knowledge of the Stroh formalism and the Lekhnitskii formalism for two-dimensional anisotropic elasticity as well as the complex variable formalism developed by Lekhnitskii for plate bending problems, in this paper a Stroh-like formalism for the bending theory of anisotropic plates is established. The key feature that makes the Stroh formalism more attractive than the Lekhnitskii formalism is that the former possesses the eigenrelation that relates the eigenmodes of stress functions and displacements to the material properties. To retain this special feature, the associated eigenrelation and orthogonality relation have also been obtained for the present formalism. By intentional rearrangement, this new formalism and its associated relations look almost the same as those for the two-dimensional problems. Therefore, almost all the techniques developed for the two-dimensional problems can now be applied to the plate bending problems. Thus, many unsolved plate bending problems can now be solved if their corresponding two-dimensional problems have been solved successfully. To illustrate this benefit, two simple examples are shown in this paper. They are anisotropic plates containing elliptic holes or inclusions subjected to out-of-plane bending moments. The results are simple, exact and general. Note that the anisotropic plates treated in this paper consider only the homogeneous anisotropic plates. If a composite laminate is considered, it should be a symmetric laminate to avoid the coupling between stretching and bending behaviors.

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Kochanek, T., and W. Wyrobek-Kochanek. "Almost orthogonally additive functions." Journal of Mathematical Analysis and Applications 400, no. 1 (April 2013): 1–14. http://dx.doi.org/10.1016/j.jmaa.2012.11.009.

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Joswig, Julia S., Christian Wirth, Meredith C. Schuman, Jens Kattge, Björn Reu, Ian J. Wright, Sebastian D. Sippel, et al. "Climatic and soil factors explain the two-dimensional spectrum of global plant trait variation." Nature Ecology & Evolution 6, no. 1 (December 23, 2021): 36–50. http://dx.doi.org/10.1038/s41559-021-01616-8.

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AbstractPlant functional traits can predict community assembly and ecosystem functioning and are thus widely used in global models of vegetation dynamics and land–climate feedbacks. Still, we lack a global understanding of how land and climate affect plant traits. A previous global analysis of six traits observed two main axes of variation: (1) size variation at the organ and plant level and (2) leaf economics balancing leaf persistence against plant growth potential. The orthogonality of these two axes suggests they are differently influenced by environmental drivers. We find that these axes persist in a global dataset of 17 traits across more than 20,000 species. We find a dominant joint effect of climate and soil on trait variation. Additional independent climate effects are also observed across most traits, whereas independent soil effects are almost exclusively observed for economics traits. Variation in size traits correlates well with a latitudinal gradient related to water or energy limitation. In contrast, variation in economics traits is better explained by interactions of climate with soil fertility. These findings have the potential to improve our understanding of biodiversity patterns and our predictions of climate change impacts on biogeochemical cycles.

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Thas, Koen. "Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion." Symmetry 11, no. 2 (February 2, 2019): 174. http://dx.doi.org/10.3390/sym11020174.

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In a recent paper, Chang et al. have proposed studying “quantum F u n ”: the q ↦ 1 limit of modal quantum theories over finite fields F q , motivated by the fact that such limit theories can be naturally interpreted in classical quantum theory. In this letter, we first make a number of rectifications of statements made in that paper. For instance, we show that quantum theory over F 1 does have a natural analogon of an inner product, and so orthogonality is a well-defined notion, contrary to what was claimed in Chang et al. Starting from that formalism, we introduce time evolution operators and observables in quantum F u n , and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F u n . Finally, we obtain a no-deletion result as well. Remarkably, we show that we can perform quantum deletion by almost unitary operators, with a probability tending to 1. Although we develop the construction in quantum F u n , it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces).

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Raupp, Carlos F. M., André S. W. Teruya, and Pedro L. Silva Dias. "Linear and Weakly Nonlinear Energetics of Global Nonhydrostatic Normal Modes." Journal of the Atmospheric Sciences 76, no. 12 (November 25, 2019): 3831–46. http://dx.doi.org/10.1175/jas-d-19-0131.1.

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Abstract Here the theory of global nonhydrostatic normal modes has been further developed with the analysis of both linear and weakly nonlinear energetics of inertia–acoustic (IA) and inertia–gravity (IG) modes. These energetics are analyzed in the context of a shallow global nonhydrostatic model governing finite-amplitude perturbations around a resting, hydrostatic, and isothermal background state. For the linear case, the energy as a function of the zonal wavenumber of the IA and IG modes is analyzed, and the nonhydrostatic effect of vertical acceleration on the IG waves is highlighted. For the nonlinear energetics analysis, the reduced equations of a single resonant wave triad interaction are obtained by using a pseudoenergy orthogonality relation. Integration of the triad equations for a resonance involving a short harmonic of an IG wave, a planetary-scale IA mode, and a short IA wave mode shows that an IG mode can allow two IA modes to exchange energy in specific resonant triads. These wave interactions can yield significant modulations in the dynamical fields associated with the physical-space solution with periods varying from a daily time scale to almost a month long.

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Chinchilla-Romero, Natalia, Jorge Navarro-Ortiz, Pablo Muñoz, and Pablo Ameigeiras. "Collision Avoidance Resource Allocation for LoRaWAN." Sensors 21, no. 4 (February 9, 2021): 1218. http://dx.doi.org/10.3390/s21041218.

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The number of connected IoT devices is significantly increasing and it is expected to reach more than two dozens of billions of IoT connections in the coming years. Low Power Wide Area Networks (LPWAN) have become very relevant for this new paradigm due to features such as large coverage and low power consumption. One of the most appealing technologies among these networks is LoRaWAN. Although it may be considered as one of the most mature LPWAN platforms, there are still open gaps such as its capacity limitations. For this reason, this work proposes a collision avoidance resource allocation algorithm named the Collision Avoidance Resource Allocation (CARA) algorithm with the objective of significantly increase system capacity. CARA leverages the multichannel structure and the orthogonality of spreading factors in LoRaWAN networks to avoid collisions among devices. Simulation results show that, assuming ideal radio link conditions, our proposal outperforms in 95.2% the capacity of a standard LoRaWAN network and increases the capacity by almost 40% assuming a realistic propagation model. In addition, it has been verified that CARA devices can coexist with LoRaWAN traditional devices, thus allowing the simultaneous transmissions of both types of devices. Moreover, a proof-of-concept has been implemented using commercial equipment in order to check the feasibility and the correct operation of our solution.

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Nilsen, Halvor M., K. A. A. Lie, and Jostein R. Natvig. "Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods." SPE Journal 17, no. 02 (June 7, 2012): 568–79. http://dx.doi.org/10.2118/149690-pa.

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Summary The predominant way of modeling faults in industry-standard flow simulators is to introduce so-called transmissibility multipliers in the underlying two-point discretization. Although this approach provides adequate accuracy in many practical cases, two-point discretizations are only consistent for K-orthogonal grids and may introduce significant discretization errors for grids that severely depart from being K-orthogonal. Such grid-distortion errors can be avoided by lateral or vertical stair-stepping of deviated faults at the expense of errors in the geometrical fault description. In other words, modelers have the choice of either making (geometrical) errors by adapting faults to a grid that is almost K-orthogonal, or introducing discretization errors because of the lack of K-orthogonality if the grid is adapted to deviated faults. We propose a method for accurate description of faults in solvers based on a hybridized mixed or mimetic discretization, which also includes the MPFA-O method. The key idea is to represent faults as internal boundaries and calculate fault transmissibilities directly instead of using multipliers to modify grid-dependent transmissibilities. The resulting method is geology-driven and consistent for cells with planar surfaces and thereby avoids the grid errors inherent in the two-point method. We also propose a method to translate fault transmissibility multipliers into fault transmissibilities. This makes our method readily applicable to reservoir models that contain fault multipliers.

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Wu, Jin, Ming Liu, Chengxi Zhang, Yulong Huang, and Zebo Zhou. "Geomagnetic orbit determination: EKF or UKF?" Aircraft Engineering and Aerospace Technology 93, no. 6 (July 26, 2021): 985–94. http://dx.doi.org/10.1108/aeat-11-2020-0279.

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Purpose Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion. Design/methodology/approach This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model. Findings While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination. Practical implications The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models. Originality/value The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.

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Li, Zhongyang, Silei Wang, Mengtao Wang, Bin Yuan, and Pibin Bing. "Simultaneous Generation of Two Orthogonally Polarized Terahertz Waves by Stimulated Polariton Scattering with a Periodically Poled LiNbO3 Crystal." Crystals 8, no. 8 (July 24, 2018): 304. http://dx.doi.org/10.3390/cryst8080304.

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We present a theoretical investigation of the simultaneous generation of two orthogonally polarized terahertz (THz) waves by stimulated polariton scattering (SPS) with a periodically poled LiNbO3 (PPLN) crystal. The two orthogonally polarized THz waves are generated from SPS with A1 and E symmetric transverse optical (TO) modes in a LiNbO3 crystal, respectively. The parallel polarized THz wave is generated from A1 symmetric TO modes with type-0 phase-matching of e = e + e, and the perpendicular polarized THz wave is generated from E symmetric TO modes with type-I phase-matching of e = o + o. The two types of phase-matching of e = e + e and e = o + o can be almost satisfied simultaneously by accurately selecting the poling period of the PPLN crystal. We calculate the photon flux density of the two orthogonally polarized THz waves by solving the coupled wave equations. The calculation results indicate that the two orthogonally polarized THz waves can be efficiently generated, and the relative intensities between the two orthogonally polarized THz waves can be modulated.

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Hamilton, Martin. "Finitary Group Cohomology and Group Actions on Spheres." Proceedings of the Edinburgh Mathematical Society 51, no. 3 (October 2008): 651–55. http://dx.doi.org/10.1017/s0013091507000430.

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AbstractWe show that if G is an infinitely generated locally (polycyclic-by-finite) group with cohomology almost-everywhere finitary, then every finite subgroup of G acts freely and orthogonally on some sphere.

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Jumpathong, Juangjun, Pascal Retailleau, Muna Ali Abdalla, Jamal Ouazzani, and Saisamorn Lumyong. "2-Butyl-5-pentylbenzene-1,3-diol." Acta Crystallographica Section E Structure Reports Online 65, no. 6 (May 23, 2009): o1366. http://dx.doi.org/10.1107/s1600536809018820.

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In the title compound, C15H24O2, a natural dialkylresorcinol commonly named stemphol, the molecules are linked intoC(6) andC22(4) chains andR44(16) rings by intermolecular O—H...O hydrogen bonds, creating molecular sheets parallel to the (010) plane. The alkyl chains are directed orthogonally away from these planes in almost complete extension.

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CRASMAREANU, MIRCEA. "DIRAC STRUCTURES FROM LIE INTEGRABILITY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1220005. http://dx.doi.org/10.1142/s0219887812200058.

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We prove that a pair (F = vector sub-bundle of TM, its annihilator) yields an almost Dirac structure which is Dirac if and only if F is Lie integrable. Then a flat Ehresmann connection on a fiber bundle ξ yields two complementary, but not orthogonally, Dirac structures on the total space M of ξ. These Dirac structures are also Lagrangian sub-bundles with respect to the natural almost symplectic structure of the big tangent bundle of M. The tangent bundle in Riemannian geometry is discussed as particular case and the 3-dimensional Heisenberg space is illustrated as example. More generally, we study the Bianchi–Cartan–Vranceanu metrics and their Hopf bundles.

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Ma, Xiyue, Kean Chen, and Jian Xu. "Active Control of Sound Transmission through Orthogonally Rib Stiffened Double-Panel Structure: Mechanism Analysis." Applied Sciences 9, no. 16 (August 10, 2019): 3286. http://dx.doi.org/10.3390/app9163286.

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Physical mechanisms of active control of sound transmission through orthogonally two ribs stiffened double-panel structure are investigated. This is the continued work of the single rib stiffened case. For the orthogonally two ribs stiffened case, four different cluster mode groups can be coupled with each other, due to the interlaced coupling effects of the horizontal and vertical ribs. One cavity mode can couple with and transmit sound energy to any type of base plate mode of the radiating ribbed plate. Consequently, the main differences of the control mechanism, when compared with the single ribbed case, lie in two aspects. One is that a novel mechanism appears. That is, suppressing and rearranging the cavity modes simultaneously achieves the suppression of the base plate modes. The other is that rearrangement of the cavity modes to rearrange the base plate modes for achieving sound radiation cancellation almost does not appear. The reason is that all types of cavity mode can couple with any one of the base plate modes due to the coupling effects of the two ribs. There is only a need to rearrange several important cavity modes to achieve suppressing the base plate mode of the radiating ribbed plate.

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Crasmareanu, Mircea. "Semi-basic 1-forms and courant structure for metrizability problems." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 153–63. http://dx.doi.org/10.2298/pim150203020c.

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The metrizability of sprays, particularly symmetric linear connections, is studied in terms of semi-basic 1-forms using the tools developed by Bucataru and Dahl in [2]. We introduce a type of metrizability in relationship with the Finsler and projective metrizability. The Lagrangian corresponding to the Finsler metrizability as well as the Bucataru{Dahl characterization of Finsler and projective metrizability are expressed by means of the Courant structure on the big tangent bundle of TM. A byproduct of our computations is that a at Riemannian metric, or generally an R-at Finslerian spray, yields two complementary, but not orthogonally, Dirac structures on TbigTM. These Dirac structures are also Lagrangian subbundles with respect to the natural almost symplectic structure of TbigTM.

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Chen, Shi, Qing-Yuan Zhao, Kai Zheng, Xu Tao, Jia-Wei Guo, Zhen Liu, Hui Wang, et al. "Stacking two superconducting nanowire single-photon detectors via membrane microchip transfer." Applied Physics Letters 121, no. 11 (September 12, 2022): 112601. http://dx.doi.org/10.1063/5.0118213.

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Multilayer superconducting nanowire single-photon detectors (SNSPDs) have exhibited several advantages, such as increased detection efficiency, reduced polarization sensitivity, and scaling up to large arrays. However, monolithic fabrication of such multilayer devices is challenging. In this work, a hybrid integration method has been introduced by etching SNSPDs into the membrane microchips, followed by the pick and place transferring process. This method has been verified by stacking two SNSPDs orthogonally. Both detectors show near saturated detection efficiencies and low timing jitters. Furthermore, thermal coupling effects have been observed between the two SNSPDs. The photon detection pulses from either detector can trigger the other one almost deterministically with a latency of several nanoseconds. This method offers a flexible way to fabricate multilayer SNSPDs or integrate them with other heterogeneous devices.

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Bozinovic, Nenad, Yang Yue, Yongxiong Ren, Moshe Tur, Poul Kristensen, Hao Huang, Alan E. Willner, and Siddharth Ramachandran. "Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers." Science 340, no. 6140 (June 27, 2013): 1545–48. http://dx.doi.org/10.1126/science.1237861.

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Internet data traffic capacity is rapidly reaching limits imposed by optical fiber nonlinear effects. Having almost exhausted available degrees of freedom to orthogonally multiplex data, the possibility is now being explored of using spatial modes of fibers to enhance data capacity. We demonstrate the viability of using the orbital angular momentum (OAM) of light to create orthogonal, spatially distinct streams of data-transmitting channels that are multiplexed in a single fiber. Over 1.1 kilometers of a specially designed optical fiber that minimizes mode coupling, we achieved 400-gigabits-per-second data transmission using four angular momentum modes at a single wavelength, and 1.6 terabits per second using two OAM modes over 10 wavelengths. These demonstrations suggest that OAM could provide an additional degree of freedom for data multiplexing in future fiber networks.

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Betsch, Tilmann, Madlen Glauer, Frank Renkewitz, Isabell Winkler, and Peter Sedlmeier. "Encoding, storage and judgment of experienced frequency and duration." Judgment and Decision Making 5, no. 5 (August 2010): 347–64. http://dx.doi.org/10.1017/s1930297500002151.

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AbstractThis paper examines conditions that do or do not lead to accurate judgments of frequency (JOF) and judgments of duration (JOD). In three experiments, duration and frequency of visually presented stimuli are varied orthogonally in a within-subjects design. Experiment 1 reveals an asymmetric judgment pattern. JOFs reflected actual presentation frequency quite accurately and were unbiased by exposure duration. Conversely, JODs were almost insensitive to actual exposure duration and were systematically biased by presentation frequency. We show, however, that a tendency towards a symmetric judgment pattern can be obtained by manipulating encoding conditions. Sustaining attention during encoding (Experiment 2) or enhancing richness of the encoded stimuli (Experiment 3) increases judgment sensitivity in JOD and yields biases in both directions (JOF biased by exposure duration, JOD biased by presentation frequency). The implications of these findings for underlying memory mechanisms are discussed.

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Morganti, R., E. M. Sadler, T. A. Oosterloo, A. Pizzella, and F. Bertola. "The HI-rich Elliptical Galaxy NGC 5266: An Old Merger Remnant?" Publications of the Astronomical Society of Australia 14, no. 1 (1997): 89–91. http://dx.doi.org/10.1071/as97089.

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AbstractWe present HI images for the dust-lane elliptical galaxy NGC 5266. This galaxy contains more than 1010M☉ of HI and our data show that the neutral hydrogen extends to ∼8 arcmin each side of the nucleus, or eight times the optical half-light radius Re. Surprisingly, the outer HI gas extends almost orthogonally to the optical dust lane. The overall HI kinematics can be successfully modelled by assuming that the gas hes in two orthogonal planes—in the plane of the dust lane in the central parts and perpendicular to this in the outer regions. The large amount of neutral gas observed and the HI morphology suggest that this object may have formed from the merger of two gas rich spiral galaxies. If so, it probably represents a relatively old merger remnant since most of the HI appears settled. The mass-to-light ratio has also been derived, with evidence for a dark matter halo around this galaxy.

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Omar, Siti Aminah, Chee Keong Chah, Thahira B. S. A. Ravoof, Mukesh M. Jotani, and Edward R. T. Tiekink. "S-Benzyl 3-[1-(6-methylpyridin-2-yl)ethylidene]dithiocarbazate: crystal structure and Hirshfeld surface analysis." Acta Crystallographica Section E Crystallographic Communications 74, no. 2 (January 31, 2018): 261–66. http://dx.doi.org/10.1107/s2056989018001330.

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In the title dithiocarbazate ester, C16H17N3S2 (systematic name: (Z)-{[(benzylsulfanyl)methanethioyl]amino}[1-(6-methylpyridin-2-yl)ethylidene]amine), the central methylidenehydrazinecarbodithioate (C2N2S2) core is almost planar (r.m.s. deviation = 0.0111 Å) and forms dihedral angles of 71.67 (3)° with the approximately orthogonally inclined thioester phenyl ring, and 7.16 (7)° with the approximately coplanar substituted pyridyl ring. The latter arrangement and the Z configuration about the imine-C=N bond allows for the formation of an intramolecular hydrazine-N—H...N(pyridyl) hydrogen bond that closes an S(6) loop. In the crystal, phenyl-C—H...S(thione), methylene-C—H...π(pyridyl), methylene- and phenyl-C—H...π(phenyl) contacts connect molecules into supramolecular layers propagating in the bc plane; the layers stack along the a axis with no directional interactions between them. The analysis of the Hirshfeld surface indicates the relative importance of an intralayer phenyl-H...H(pyridyl) contact upon the molecular packing.

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Haynes, J. D., G. Roth, M. Stadler, and H. J. Heinze. "Neuromagnetic Correlates of Perceived Contrast in Primary Visual Cortex." Journal of Neurophysiology 89, no. 5 (May 1, 2003): 2655–66. http://dx.doi.org/10.1152/jn.00820.2002.

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When a target grating is flashed into a larger, surrounding grating, its contrast is perceived to be lower when both gratings are oriented collinearly rather than orthogonally. This effect can be used to dissociate the perceived contrast from the physical contrast of a target grating. We recorded the transient electric potentials and magnetic fields evoked by flashed target gratings and compared them with psychophysical judgments of perceived contrast. Both early (100 ms) and late (150 ms) transients were reduced in amplitude when targets were flashed into a collinear rather than orthogonal surround, thus paralleling the reduction in perceived contrast. Although targets in orthogonal backgrounds required 40% lower physical contrast to match the perceived contrast of collinear targets, the amplitudes of electrophysiological transients of matching stimuli were almost identical. Thus the responses correlated better with perceived than with physical target contrast. This holds especially for the late transient response. Source localization indicated that the transients in question may originate in primary visual cortex. Our results therefore identify the activity of primary visual cortex as one possible neural correlate of perceived contrast.

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Journal articles on the topic 'Almost orthogonality'

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