Odd Index Research Articles

An efficient subcarrier arrangement for airborne OFDM communication using parametric loudspeaker

Acoustic communication in air has attracted attention as an alternative near-field communication medium. A parametric loudspeaker has the potential to achieve acoustic communication within a personal area. However, secondary nonlinear components of communication signals generated by self-demodulation in air become barriers to acoustic communication. Although the use of orthogonal frequency division multiplexing (OFDM) would be desirable, since it achieves low-calculation-cost equalization at the receiver even in a multipath fading environment, inter-carrier interference (ICI) with secondary components degrades communication quality. In this paper, we propose an efficient subcarrier arrangement for OFDM communication using parametric loudspeakers. We consider two subcarrier arrangements: odd-comb OFDM and narrow-band OFMD. The former has an active subcarrier at odd indexes, and the latter has a restricted frequency band to avoid ICI. We also test the proposed schemes in experiments. The experimental results suggest that the proposed OFDM successfully improves communication quality compared to the original OFDM.

On Generalized Fibonacci Numbers

Fibonacci numbers and their polynomials have been generalized mainly by two ways: by maintaining the recurrence relation and varying the initial conditions, and by varying the recurrence relation and maintaining the initial conditions. In this paper, we introduce and derive various properties of $r$-sum Fibonacci numbers. The recurrence relation is maintained but initial conditions are varied. Among results obtained are Binet's formula, generating function, explicit sum formula, sum of first $n$ terms, sum of first $n$ terms with even indices, sum of first $n$ terms with odd indices, alternating sum of $n$ terms of $r-$sum Fibonacci sequence, Honsberger's identity, determinant identities and a generalized identity from which Cassini's identity, Catalan's identity and d'Ocagne's identity follow immediately.

Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

Abstract A subgroup H of a group G is said to be pronormal in G if H and H g {H^{g}} are conjugate in 〈 H , H g 〉 {\langle H,H^{g}\rangle} for every g ∈ G {g\in G} . In this paper, we determine the finite simple groups of type E 6 ⁢ ( q ) {E_{6}(q)} and E 6 2 ⁢ ( q ) {{}^{2}E_{6}(q)} in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

Maximal solvable subgroups of odd index in symmetric groups

Maximal solvable subgroups of odd index in symmetric groups

Ионный транспорт в гидратированных соединениях на основе полисурьмяной кристаллической кислоты

The present work is devoted to the study of crystalline polyantimonic acid (CPA) structural properties in conditions of ion exchange and heat treatment of its substituted Ag+, H+-forms. According to the obtained data of X-ray diffraction qualitative phase analysis, the compounds analyzed crystallize within the framework of the pyrochlore type structure (space group Fd-3m). For phases being isomorphic to this structural type, it was shown that with an increase in the degree of substitution α, a relative intensity redistribution of the group of reflections with even and odd indices and decrease of unit cell parameter a were observed.. The data of thermogravimetric analysis allows to conclude that the thermolysis of CPA’s ion-substituted forms proceeds in a wide temperature range from 297 to 973 K being accompanied by a decrease of samples weight. Applying the Rietveld method, the structural characteristics of CPA and its derivatives were refined, and a model of populating the corresponding metal ions by crystallographic positions within a pyrochlore-type structure was proposed. Using a complex of physicochemical methods (thermogravimetric and X-ray diffraction analyses), the effect of hydration of CPA compounds with a pyrochlore type structure on transport properties was determined. It is shown that with an increase of substitution degree α in samples of CPA’s Ag+, H+-forms in conditions of alternating current the value of the specific conductivity decreases monotonically. An increase of silver ions content in the phases of Ag+, H+-forms leads to the change of proton-binding energy with the crystal lattice. In the condition of elevated temperature in hydrated CPA compounds, charge transfer is performed by silver ions. It was found that the electrical conductivity in the samples analyzed can also rise with a silver ions amount decrease (16d-positions are partially filled with Sb3+).

Maximal Solvable Subgroups of Odd Index in Symmetric Groups

Maximal solvable subgroup subgroup of odd index. Maximal solvable subgroups of odd index in symmetric groups are classified up to conjugation.

Improving Oil Recovery Through Fracture Injection and Production of Multiple Fractured Horizontal Wells

Abstract Well production rates decline quickly in the tight reservoirs, and enhanced oil recovery (EOR) is needed to increase productivity. Conventional flooding from adjacent wells is inefficient in the tight formations, and Huff-n-Puff also fails to achieve the expected productivity. This paper investigates the feasibility of the inter-fracture injection and production (IFIP) method to increase oil production rates of horizontal wells. Three multi-fractured horizontal wells (MFHWs) are included in a cluster well. The fractures with even and odd indexes are assigned to be injection fractures (IFs) and recovery fractures (RFs). The injection/production schedule includes synchronous inter-fracture injection and production (s-IFIP) and asynchronous inter-fracture injection and production (a-IFIP). The production performances of three MFHWs are compared by using four different recovery approaches based on numerical simulation. Although the number of RFs is reduced by about 50% for s-IFIP and a-IFIP, they achieve much higher oil rates than depletion and CO2 Huff-n-Puff. The sensitivity analysis is performed to investigate the impact of parameters on IFIP. The spacing between IFs and RFs, CO2 injection rates, and connectivity of fracture networks affect oil production significantly, followed by the length of RFs, well spacing among MFHWs, and the length of IFs. The suggested well completion scheme for the IFIP methods is presented. This work discusses the ability of the IFIP method in enhancing the oil production of MFHWs.

The asymptotic Connes–Moscovici characteristic map and the index cocycles

We show that the (even and odd) index cocycles for theta-summable Fredholm modules are in the image of the Connes-Moscovici characteristic map. To show this, we first define a new range of asymptotic cohomologies, and then we extend the Connes-Moscovici characteristic map to our setting. The ordinary periodic cyclic cohomology and the entire cyclic cohomology appear as two instances of this setup. We then construct an asymptotic characteristic class, defined independently from the underlying Fredholm module. Paired with the $K$-theory, the image of this class under the characteristic map yields a non-zero scalar multiple of the index in the even case, and the spectral flow in the odd case.

Solubility of Finite Generalized Frobenius with the Kernel of Odd Index

A finite group $$G$$ is said to be a generalized Frobenius group with kernel$$F$$, if $$F$$ is a proper nontrivial normal subgroup of $$G$$ and for every element $$Fx$$ of prime order of the quotient group $$G/F$$ the coset $$Fx$$ of the group $$G$$ over $$F$$ has only $$p$$-elements for some prime $$p$$ depending on $$x$$. This article considers generalized Frobenius groups with insoluble kernel. We prove that a quotient group of a generalized Frobenius group over its insoluble kernel is a 2-group.

Quadratic cosine-Gauss beams – the new family of localized solutions of the paraxial wave equation

We propose a new class of localized solutions of the paraxial wave equation. They have a form of a product of a Gaussian term and an amplitude which contains only elementary coordinate functions. Solutions are obtained by summing of the quadratic Bessel–Gauss beams with odd indices. Due to the configuration of the obtained solutions, we named them quadratic cosine-Gauss beams.

Pell graphs

In this paper, we introduce the Pell graphs, a new family of graphs similar to the Fibonacci cubes. They are defined on certain ternary strings (Pell strings) and turn out to be subgraphs of Fibonacci cubes of odd index. Moreover, as well as ordinary hypercubes and Fibonacci cubes, Pell graphs have several interesting structural and enumerative properties. Here, we determine some of them. Specifically, we obtain a canonical decomposition giving a recursive structure, some basic properties (bipartiteness and existence of maximal matchings), some metric properties (radius, diameter, center, periphery, medianicity), some properties on subhypercubes (cube coefficients and polynomials, cube indices, decomposition in subhypercubes), and, finally, the distribution of the degrees.

Primitive characters of maximal subgroups of M-groups

Let [Formula: see text] be a maximal subgroup of an [Formula: see text]-group [Formula: see text] with odd index and let [Formula: see text] be primitive. Lewis proved in this situation that [Formula: see text] divides [Formula: see text], and Isaacs and Wilde further refined this result by showing that either [Formula: see text] or [Formula: see text]. In this paper, we present an independent and simpler proof for these remarkable results and thereby obtain more detailed information regarding the structure of the group [Formula: see text] and the primitive character [Formula: see text]. In particular, [Formula: see text] is strongly irreducible in the sense of Brauer.

Diffraction from two-dimensional orthogonal nonseparable periodic structures: Talbot distance dependence on the number theoretic properties of the structures.

In this work, the diffraction-based discrimination of two-dimensional (2D) orthogonal separable and nonseparable periodic structures and prediction of the reduced Talbot distances for 2D orthogonal nonseparable periodic structures are presented. 2D orthogonal periodic structures are defined and classified into separable (multiplicative or additive) and nonseparable categories with the aid of a spatial spectrum lattice. For both the separable and nonseparable cases, the spatial spectra or far-field impulses are 2D orthogonal lattices. We prove that for a 2D orthogonal separable structure, in addition to the DC impulse, there are other impulses on the coordinate axes. As a result, if all the spectrum impulses of a structure on the coordinate axes, except for the DC impulse, vanish, we conclude that the structure is nonseparable. In the second part of this work, using a unified formulation, the near-field diffraction of the 2D orthogonal separable and nonseparable periodic structures is investigated. In general, the Talbot distance equals the least common multiple of the individual Talbot distances in the orthogonal directions, say, z t =z lcm . For the 2D orthogonal nonseparable periodic structures having Fourier coefficients only with odd indices, we have found surprising results. It is shown that for this kind of structure, the Talbot distance strongly depends on the number theoretic properties of the structure. Depending on the ratio of the structure's periods in the orthogonal directions, pxpy, the Talbot distance reduces to z lcm 2, z lcm 4, or z lcm 8. In addition, for the 2D orthogonal nonseparable sinusoidal grating, we show that, regardless of the value of pxpy, self-images are formed at distances smaller than the conventional Talbot distances attributed to px and py that we name the reduced Talbot (RT) distances. Halfway between two adjacent RT distances, the formation of negative self-images with a complementary amplitude of the self-images is predicted. Halfway between two adjacent self-image and negative-elf-image, subimages are formed. As another interesting result, we show that the intensity patterns of the subimages are 2D multiplicatively separable with halved periods in both directions. Finally, we show that 2D almost periodic structures with impulses on zone-plate-like concentric circles have self-images under plane wave illumination.

Regular switching components

We consider a problem of Discrete Tomography which consists of reconstructing a finite lattice set S⊂Z2 from given horizontal and vertical X-rays (i.e. with prescribed numbers of points in each row and column). Without additional requirements, the problem can be solved in polynomial time. Many variants require the solution to be in a chosen class A. For instance, the problem is NP-complete for the class A=H∩V of HV-convex lattice sets and it is polynomial for the class A=H∩V∩P of HV-convex polyominoes. Twenty years after these results, the problem's complexity remains unknown for A=C, the class of C-convex lattice sets (i.e. two-dimensional lattice polytopes).The main difficulty to solve this problem comes from combinatorial structures called switching components. Switching components are closed path with horizontal and vertical edges such that the solutions S are composed of either the elements of even or of odd indices. This binary choice can be encoded by a Boolean variable associated with the switching component and the convexity constraints are simply encoded by SAT clauses (2-clauses for HV-convexity and 3-clauses for C-convexity).The purpose of the paper is to investigate the properties of the switching components and the consequences of the convexity requirements. We divide the switching components in two classes: regular if their turning angle is constant, irregular otherwise. We prove that adjacent regular switching components have the same Boolean values. This property allows us to merge them into extended switching components. We prove that if all switching components are regular, then the extended switching components are all independent (then the number of solutions with the considered feet is 2n, where n is the number of extended switching components). Finally, we prove that they are geometrically ordered.

On Pronormal Subgroups in Finite Simple Groups

A subgroup H of a group G is called pronormal if, for any element g of G, the subgroups H and Hg are conjugate in the subgroup they generate. Some problems in the theory of permutation groups and combinatorics have been solved in terms of pronormality, and the characterization of pronormal subgroups in finite groups is a problem of importance for applications of group theory. A task of special interest is the study of pronormal subgroups in finite simple groups and direct products of such groups. In 2012 E.P. Vdovin and D.O. Revin conjectured that the subgroups of odd index in all finite simple groups are pronormal. We disproved this conjecture in 2016. Accordingly, a natural task is to classify finite simple groups in which the subgroups of odd index are pronormal. This paper completes the description of finite simple groups whose Sylow 2-subgroups contain their centralizers in the group and the subgroups of odd index in which are pronormal.

Toeplitz operators and the Roe–Higson type index theorem

Let M be a complete Riemannian manifold and assume that M is partitioned by a hypersurface N . In this paper we introduce a novel class of functions C_{\mathrm{w}}(M) on noncompact manifolds, which is slightly larger than the algebra of Higson functions. Out of \phi that belongs to C_{\mathrm{w}}(M) we construct an index class Ind (\phi , D) in K_{1} -group of the Roe algebra of M by using the Kasparov product. It is supposed to be a counterpart of Roe's odd index class. We finally prove that Connes' pairing of \mathrm{Ind}(\phi , D) and Roe's cyclic 1 -cocycle is equal to the Fredholm index of a Toeplitz operator on N . This is an extension of the Roe–Higson index theorem to even-dimensional partitioned manifolds.

On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups

We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).

On the unit group of the Burnside ring as a biset functor for some solvable groups

The theory of bisets has been very useful in progress towards settling the longstanding question of determining units for the Burnside ring. In 2006 Bouc used bisets to settle the question for p-groups. In this paper, we provide a standard basis for the unit group of the Burnside ring for groups that contain a abelian subgroups of index two. We then extend this result to groups G, where G has a normal subgroup, N, of odd index, such that N contains an abelian subgroups of index 2. Next, we study the structure of the unit group of the Burnside ring as a biset functor, B× on this class of groups and determine its lattice of subfunctors. We then use this to determine the composition factors of B× over this class of groups. Additionally, we give a sufficient condition for when the functor B×, defined on a class of groups closed under subquotients, has uncountably many subfunctors.

Power Allocation for OFDM Over Multi-scale Multi-lag Channels

Underwater acoustic (UWA) signal is wideband in nature and suffers doubly selective fading in time and frequency. In the presence of relative motion, a typical UWA channel can be described by a multiscale multilag (MSML) model. To compensate the scaling effect of UWA channels, many UWA communication systems employ a signal-resampling operation by a single scale at the front end of the receiver. For orthogonal frequency division multiplexing systems, since the path scales are different from each other, the resampling can alleviate but not clean out the intercarrier interference (ICI) resulting from the MSML channel. In this paper, we first describe the resampled signal by an equivalent MSML model with residual time scales, which are much smaller than that of the original MSML channel. With the given statistical parameters of the equivalent MSML channel, the closed-form expressions of the average subchannel gains and ICI coefficients are derived. Based on the ICI coefficients, we derive the analytical expression of a lower bound on the average achievable rate of the system as a function of the power allocation. We then investigate the power allocation to improve the lower bound on the achievable rate. Our key idea is that, on subcarriers whose ICIs dominate the additive noise, nothing is transmitted to avoid low energy efficiency. After proving that the ICI coefficient increases monotonically as the subcarrier frequency rises, we propose an ON–OFF uniform power allocation method, in which subcarriers with odd indices keep inactive starting from a certain index to avoid ICI. The performance of the proposed power allocation is evaluated via numerical simulations, whose results show that the proposed method outperforms the existing methods when the residual time scales cannot be neglected.

Nonabelian Composition Factors of a Finite Group Whose Maximal Subgroups of Odd Indices Are Hall Subgroups

We obtain a description of nonabelian composition factors of a finite nonsolvable group in which any maximal subgroup of odd index is a Hall subgroup.