Orthogonal Type Research Articles

Period Relations Between the Betti–Whittaker Periods for GLn Under Duality

Abstract In this paper, under some regularity conditions, we prove a period relation between the Betti–Whittaker periods associated to a regular algebraic cuspidal automorphic representation of $\operatorname{GL}_{n}({{\mathbb{A}}})$ and its contragredient. As a consequence, we prove the trivialness of the relative period associated to a regular algebraic cuspidal automorphic representation of $\operatorname{GL}_{2n}({{\mathbb{A}}})$ of orthogonal type, which implies the algebraicity of the ratios of successive critical $L$-values for $\textrm{GSpin}_{2n}^{*} \times \operatorname{GL}_{n^{\prime}}$ by the result of Harder and Raghuram.

Diverse and abundant phages exploit conjugative plasmids

Phages exert profound evolutionary pressure on bacteria by interacting with receptors on the cell surface to initiate infection. While the majority of phages use chromosomally encoded cell surface structures as receptors, plasmid-dependent phages exploit plasmid-encoded conjugation proteins, making their host range dependent on horizontal transfer of the plasmid. Despite their unique biology and biotechnological significance, only a small number of plasmid-dependent phages have been characterized. Here we systematically search for new plasmid-dependent phages targeting IncP and IncF plasmids using a targeted discovery platform, and find that they are common and abundant in wastewater, and largely unexplored in terms of their genetic diversity. Plasmid-dependent phages are enriched in non-canonical types of phages, and all but one of the 65 phages we isolated were non-tailed, and members of the lipid-containing tectiviruses, ssDNA filamentous phages or ssRNA phages. We show that plasmid-dependent tectiviruses exhibit profound differences in their host range which is associated with variation in the phage holin protein. Despite their relatively high abundance in wastewater, plasmid-dependent tectiviruses are missed by metaviromic analyses, underscoring the continued importance of culture-based phage discovery. Finally, we identify a tailed phage dependent on the IncF plasmid, and find related structural genes in phages that use the orthogonal type 4 pilus as a receptor, highlighting the evolutionarily promiscuous use of these distinct contractile structures by multiple groups of phages. Taken together, these results indicate plasmid-dependent phages play an under-appreciated evolutionary role in constraining horizontal gene transfer via conjugative plasmids.

A mini review on the ballistic protection performance of 2D and 3D woven fabric structures woven from technical yarns for body armormaterials in military application

This mini-compilation study included a review study conducted on the ballistic protection performances of 2D and 3D structured woven fabric structures for body armor materials in military applications. As conclusion, orthogonal type 3D woven fabric structures have higher ballistic protection performance compared to conventional 2D woven fabric structures by locking the high-performance yarns used and preventing slippage between layers. It is recommended to use ceramic-structured front plates such as B4C to break armor-piercing bullets, reduce penetration, and absorb a significant portion of their high kinetic energy. UHMWPE, PPD-T, and PBO technical yarns, which have fine yarn counts (between 466 dtex and 933 dtex) can be produced by 1x1 plain woven fabric construction as woven fabric structures (lamina). They must have also high warp and weft density values ​​(between 30 and 40 warp/cm and weft/cm), and orthogonal 3D woven fabric structure, high warp, and weft yarn tension (between 20 cN and 50 cN per warp yarn), 160 rpm as production speed, and multi-layered (between 13 layers and 16 layers in lamina form) in honeycomb (sandwich) geometry. Moreover, the impregnation process can be applied with CaCO3, SiO2, PVB, or CNT particles (in the particle size range of 100 nm to 400 nm) with chemicals such as PEG (in the range of 60% to 75% concentrations), in the range of 80 °C to 160 °C temperatures and between 1 hour and 3 hours. Coating (STF applications) is extremely important and successful for ballistic protection performance at IIIA, III and IV levels for NIJ standards. Future studies should include orthogonal 3D structured woven fabric applications from UHMWPE, PPD-T, or PBO technical yarns by applying STF technology in this field. They should be also examined comparatively from an experimental perspective.

Solving integral equations via orthogonal hybrid interpolative RI-type contractions

In this paper, we initiate the fixed point theorems for an orthogonal hybrid interpolative Riech Istrastescus type contractions map on orthogonal b-metric spaces to modify this class proficiently. Also, we provide some examples supporting our main results. Finally, we provide an application to solve the existence and uniqueness of an integral equation with numeric results, which is powerful in a greater way.

Moduli of polarised Enriques surfaces — Computational aspects

AbstractModuli spaces of (polarised) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to isomorphism, only finitely many different moduli spaces of polarised Enriques surfaces. Here, we investigate the possible arithmetic groups and show that there are exactly 87 such groups up to conjugacy. We also show that all moduli spaces are dominated by a moduli space of polarised Enriques surfaces of degree 1240. Ciliberto, Dedieu, Galati and Knutsen have also investigated moduli spaces of polarised Enriques surfaces in detail. We discuss how our enumeration relates to theirs. We further compute the Tits building of the groups in question. Our computation is based on groups and indefinite quadratic forms and the algorithms used are explained.

Thermomechanical Behaviors of a Novel Double-Layer Corrugated Core Structure for Thermal Protection System

Corrugated core sandwich structures have great potential in the application to thermal protection system of aerospace vehicles. However, the traditional layout of web plates could inevitably lead to thermal short effects and high risk of buckling failure of the integrated thermal protection system (ITPS). In this paper, a novel double-layer ITPS is proposed by splitting and reorganizing a classical corrugated sandwich structure without additional introducing of weight. Distribution types of parallel, symmetric, and orthogonal of the double layers are designed and studied in detail. Basic theory of the thermomechanical problem as well as finite element simulation is carried out to study the responses of the ITPS. Numerical results show that the orthogonal type has more excellent yield resistance at high temperature and large temperature gradient than the others, while the parallel type has a relatively stronger buckling resistance. In addition, the structural stiffness variation caused by temperature dependencies of material parameters is greater than that caused by thermal stress, which shows the significance of consideration of temperature-dependent material properties in structure vibration analysis.

On the superspecial loci of orthogonal type Shimura varieties

In this note, we study the superspecial loci of orthogonal type Shimura varieties of signature [Formula: see text] with [Formula: see text]. We prove a conjecture of Gross that the superspecial loci and their lift in the integral models can be parametrized by certain homogeneous spaces. As applications, we provide mass formulas for the superspecial loci. We also indicate how Gross’s conjectures can be proved in the case of Coxeter type Shimura varieties using the group theoretic methods of Görtz and He.

Hahn multiple orthogonal polynomials of type I: Hypergeometric expressions

Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kampé de Fériet hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Then, part of the Askey scheme for multiple orthogonal polynomials type I is completed. In particular, explicit expressions in terms of generalized hypergeometric series and Kampé de Fériet hypergeometric series, are given for the multiple orthogonal polynomials of type I for the Jacobi–Piñeiro, Meixner I, Meixner II, Kravchuk, Laguerre I, Laguerre II and Charlier families.

Bayesian hierarchical modeling on covariance valued data

Analysis of structural and functional connectivity (FC) of human brains is of pivotal importance for diagnosis of cognitive ability. The Human Connectome Project (HCP) provides an excellent source of neural data across different regions of interest (ROIs) of the living human brain. Individual specific data were available in the form of time varying covariance matrices representing the brain activity as the subjects perform a specific task. As a preliminary objective of studying the heterogeneity of brain connectomics across the population, we develop a probabilistic model for a sample of covariance matrices using a scaled Wishart distribution. We stress here that our data units are available in the form of covariance matrices, and we use the Wishart distribution to create our likelihood function rather than its more common usage as a prior on covariance matrices. Based on empirical explorations suggesting the data matrices to have a low effective rank, we further model the center of the Wishart distribution using an orthogonal factor model type decomposition. We encourage shrinkage toward a low rank structure through a novel shrinkage prior and discuss strategies to sample from the posterior distribution using a combination of Gibbs and slice sampling. The efficacy of the approach is explored in various simulation settings and exemplified on several case studies including our motivating HCP data. We extend our modeling framework to a dynamic setting to detect change points.

Projective Spaces as Orthogonal Modular Varieties

We construct 16 reflection groups Γ acting on symmetric domains \(\mathcal {D}\) of Cartan type IV, for which the graded algebras of modular forms are freely generated by forms of the same weight, and in particular the Satake-Baily-Borel compactification of \(\mathcal {D}/ {\Gamma }\) is isomorphic to a projective space. Four of these are previously known results of Freitag-Salvati Manni, Matsumoto, Perna and Runge. In addition we find several new modular groups of orthogonal type whose algebras of modular forms are freely generated.

Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces

In this paper, we prove fixed point theorem via orthogonal Geraghty type α-admissible contraction map in an orthogonal complete Branciari b-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically.

Generalizations of generating functions for basic hypergeometric orthogonal polynomials

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.

Efficient calculation of radiative intensity in three-dimensional atmospheres based on the Pn-IMS truncation method with a backward ray tracing system

The computational efficiency of solving the radiative transfer (RT) equation is an important issue for remote sensing and the monitoring of aerosols, clouds, and radiation, all of which involve the analysis of large volumes of data. In this study, based on the Improved Multiple and Single scattering (IMS) correction method, a backward ray tracing method was developed for the three-dimensional RT calculation (3D-IMS). We extended the IMS method to the 3D-RT problem using a backward ray tracing Monte Carlo system for calculation of both upward and downward radiance fields. In the 3D-IMS method, photons are assumed to be of two orthogonal types: one has less anisotropic scattering, while the other has highly anisotropic scattering decomposed by the delta-M method of Wiscombe (1977) to truncate a spherical harmonics expansion series. In this manner, an accurate radiance field is reconstructed by two separated ray tracings in the two independent spaces (i.e., delta-M and IMS spaces). Compared to the ordinary Monte Carlo method with the original phase function, the 3D-IMS method can better reduce the total photon number for the reconstruction of radiances. The performance of the 3D-IMS method was evaluated for plane-parallel atmospheres and for the case-4 experiment datasets of the Intercomparison of 3D Radiation Codes (I3RC) project. Among solvers included in the intercomparison, in cases with both completely backward and lateral scattering regions, the 3D-IMS method belonged to the group near the I3RC consensus mean data.

Low-lying zeros in families of elliptic curve L-functions over function fields

We investigate the low-lying zeros in families of L-functions attached to quadratic and cubic twists of elliptic curves defined over Fq(T). In particular, we present precise expressions for the expected values of traces of high powers of the Frobenius class in these families with a focus on the lower order behavior. As an application we obtain results on one-level densities and we verify that these elliptic curve families have orthogonal symmetry type. In the quadratic twist families our results refine previous work of Comeau-Lapointe. Moreover, in this case we find a lower order term in the one-level density reminiscent of the deviation term found by Rudnick in the hyperelliptic ensemble. On the other hand, our investigation is the first to treat these questions in families of cubic twists of elliptic curves and in this case it turns out to be more complicated to isolate lower order terms due to a larger degree of cancellation among lower order contributions.

Deformation and Damage Characteristics of Deep Rock Specimens Based on 3D-DIC and FBG

Abstract Specimen-scale testing of loaded rock parameters is an important research component of rock mechanics testing. In this paper, a method combining 3D-DIC and FBG (fiber Bragg grating) technology is proposed and applied to the study of deformation and damage characteristics of deep limestone and sandstone specimens under uniaxial loading conditions in the Panxie mine area of Huainan coalfield. The selection of optical fiber, the bonding method, and the process of rock specimen fabrication are introduced in detail. Two different fiber Bragg grating sensor arrays were constructed by using both multi-inclination type and orthogonal type deployment of fiber grating to dynamically monitor the strain response of rock specimens throughout the whole process. The results show that both 3D-DIC displacement monitoring and fiber Bragg grating strain captured the rock deformation and failure process well with identical outcomes. Under a continuous load of 0.3 kN/s, the local cracks of the rock specimen and the damage to the rock specimen resulted in different degrees of sudden changes in the fiber strain value. According to the differences in the degrees of brittleness and texture densities of the rock specimens, the local cracks evolution to transfixion of the limestone registered a certain time accumulation and produced more local cracks, while the sandstone at the same stage produced fewer local cracks within a shorter duration. The effective combination of regional noncontact testing and high-precision point contact can dynamically and accurately capture the rock deformation and damage characteristics at the specimen scale. In addition, the combined monitoring method of 3D-DIC and fiber grating can provide assistance in the prediction of rock crack expansion and potential fracture surfaces.

Structural and Behaviour Optimization of Tubular Structures Made of Tailor Welded Blanks by Applying Taguchi and Genetic Algorithms Methods

Even though they initially appeared as a method of using waste from other production processes, tailored welded blanks (TWB) presented several advantages by combining materials with different characteristics. On the one hand, this study focuses on minimizing the adverse effects caused by the springback of TWB parts. The proposed method is based on the Taguchi technique using orthogonal type 23 networks. On the other hand, genetic algorithms were applied to obtain maximum performance parameters within the dynamic loadings of tubular structures made of TWB by advantageous positioning of the weld line. The obtained data were compared and evaluated through software platforms such as MATLAB, Design Expert, and Dynaform, and experimental validation. By generating an objective function, the construction of thin-walled tubular structures can be controlled for a predetermined deformation and maximum energy absorption. The data obtained has an error rate of less than 3%, thus considering that this method can be used successfully in the qualitative and quantitative estimation of dynamically loaded TWB tubular structures.

A New Approximate Birkhoff Orthogonality Type

In this note, we introduce a new approximate Birkhoff orthogonality type and give a characterization for inner product spaces using the approximate orthogonality. We show some general properties of the approximate Birkhoff orthogonality type as well as applications. In particular, we study the relationship between the new approximate Birkhoff orthogonality type and other approximate orthogonality types that have been defined before. Furthermore we study the approximate preserving mapping and give some properties.

Low-lying zeros in families of holomorphic cusp forms: the weight aspect

Abstract We study low-lying zeros of L-functions attached to holomorphic cusp forms of level 1 and large even weight. In this family, the Katz–Sarnak heuristic with orthogonal symmetry type was established in the work of Iwaniec, Luo and Sarnak for test functions ϕ satisfying the condition supp$(\widehat \phi) \subset(-2,2)$. We refine their density result by uncovering lower-order terms that exhibit a sharp transition when the support of $\widehat \phi$ reaches the point 1. In particular, the first of these terms involves the quantity $\widehat \phi(1)$ which appeared in the previous work of Fouvry–Iwaniec and Rudnick in symplectic families. Our approach involves a careful analysis of the Petersson formula and circumvents the assumption of the Generalized Riemann Hypothesis (GRH) for higher-degree automorphic L-functions. Finally, when supp$(\widehat \phi)\subset (-1,1)$ we obtain an unconditional estimate which is significantly more precise than the prediction of the L-functions ratios conjecture.

Too Sensitive or Just Right?

To compare the performance of the rabbit monoclonal antihuman CD246 antibody (D5F3 clone) with the established ALK1 clone for immunohistochemical assessment of anaplastic large cell lymphoma (ALCL). Archival cases of ALCL (n = 27) were assessed immunohistochemically by use of ALK1 and D5F3 clones under standard Clinical Laboratory Improvement Amendments-compliant conditions. The intensity of cytoplasmic staining (0 = none; 1 = faint; 2 = moderate; 3+ = strong) and proportion of neoplastic cells (0%, <5%, 5%-50%, >50%) were evaluated and compared with clinical ALK break-apart fluorescence in situ hybridization (FISH) assays. Nine ALCL specimens were positive for ALK expression by ALK1 staining (33%; 1 = 1+; 0 = 2+; 8 = 3+), while 14 were positive by D5F3 staining (48%; 3 = 1+; 1 = 2+; 10 = 3+). Across the cohort, D5F3 staining showed a significantly greater proportion of cells staining positive (P = .02) and greater intensity (P = .03). Of 3 cases positive for D5F3 only with FISH results, none showed rearrangements, although 1 showed copy number gains at the ALK locus in a subset of cells. Overall, D5F3 showed greater stain intensity and proportion staining than ALK1 in ALK-positive ALCL cases, which is especially helpful in limited samples. Caution and consideration of orthogonal ALK testing types is recommended, especially for cases with weak or focal staining.

A game-theory–inspired decomposition of interspecific interaction matrices

In evolutionary game theory, pair interactions are usually defined through so-called payoff matrices, which can be decomposed as linear combinations of basis matrices that represent just four different orthogonal interaction types. In this paper, we take the first steps in exploring the utility of this decomposition in ecology. We introduce the componental cosines of the irrelevant, external, coordination, and conflict components of matrices to measure the relative weight of the different interaction types, and use them to analyse the composition of 33 experimentally obtained interspecific interaction matrices compiled from the literature, which reveals statistically significant correlations both between different components and some components and community productivity and biodiversity.