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In this article, we establish an asymptotic estimate on the number of cuspidal automorphic representations of GL 4 ( A Q ) which contribute to the cuspidal cohomology of GL 4 and are obtained from symmetric cube transfer of automorphic representations of GL 2 ( A Q ) of a given weight and with varying level structure. This generalises the recent work of C. Ambi about the similar problem for GL 3 .

The electron dynamics of atomically thin 2-D polar metal heterostructures, which consisted of a few crystalline metal atomic layers intercalated between hexagonal silicon carbide and graphene grown from the silicon carbide, were studied using nearly degenerate transient absorption spectroscopy. Optical pumping created charge carriers in both the 2-D metals and graphene components. Wavelength-dependent probing suggests that graphene-to-metal carrier transfer occurred on a sub-picosecond time scale. Following rapid (300 fs) carrier-carrier scattering, charge carriers monitored through the metal interband transition relaxed through several consecutive cooling mechanisms that included sub-picosecond carrier-phonon scattering and dissipation to the silicon carbide substrate over tens of picoseconds. By studying 2-D In, 2-D Ga, and a Ga/In alloy, we resolved accelerated electron-phonon scattering rates upon alloy formation as well as structural influences on the excitation of in-plane phonon shear modes. More rapid cooling in alloys is attributed to increased lattice disorder, which was observed through correlative polarization-resolved second harmonic generation and electron microscopy. This connection between the electronic relaxation rates, far-field optical responses, and metal lattice disorder is made possible by the intimate relation between nonlinear optical properties and atomic-level structure in these materials. These studies provided insights into electronic carrier dynamics in 2-D crystalline elemental metals, including resolving contributions from specific components of a 2-D metal-containing heterojunction. The correlative ultrafast spectroscopy and nonlinear microscopy results suggest that the energy dissipation rates can be tuned through atomic-level structures.

В отличие от классической теории научного познания, где выделялось только два уровня научного знания в любой из конкретных наук: эмпирический и теоретический, в современной эпистемологии выделяют четыре качественно различных уровня научного знания: чувственный, эмпирический, теоретический, метатеоретический. Все они отличаются друг от друга по происхождению (эпистемологии), содержанию (онтологии), методам обоснования и критериям истинности(методологии). Несмотря на то, что указанные уровни относительно независимы друг от друга, все они связаны между собой при функционировании любой конкретной науки как некоей целостной системы знания. Основной методологической процедурой обеспечения ее целостности является интерпретация. Она представляет собой конструктивноволевую деятельность мышления по идентификации содержания понятий разных уровней знания. Любая интерпретация всегда заключает в себе существенный момент риска и может быть неверной. Современная неклассическая концепция уровневой структуры научного знания позволяет осуществлять более глубокий и конкретный анализ закономерностей функционирования и развития науки по сравнению с классической эпистемологией. In contrast to the classical theory of scientific knowledge, where there were only two levels of scientific knowledge in any of the specific sciences: empirical and theoretical, in contemporary non-classical epistemology there are four qualitatively different levels of scientific knowledge: sensory, empirical, theoretical and metatheory. All of them differ in their content (ontology), means of genesis (epistemology), method of justification and criteria of truth (methodology). At the same time, although all these levels of scientific knowledge are relatively independent from each other in terms of their ontology and epistemology, they are all interrelated within the framework of the functioning of any particular science as the integrity system of knowledge. The means of achieving such integrity is a procedure of interpretation (identification) of the content of concepts of different levels of scientific knowledge. It is the constructive strong-willed activity. Every interpretation always consists of essential moment of risk and may produce an error. The non-classical approach to the level structure of scientific knowledge developed in the article allows for a deeper and more specific analysis of the laws of the functioning and development of real science, than the classical philosophy of science allowed.

We introduce a new class of values for TU-games (games with transferable utility) with a level structure, called LS-games. A level structure is a hierarchical structure where each level corresponds to a partition of the player set, which becomes increasingly coarse from the trivial partition containing only singletons to the partition containing only the grand coalition. The new values, called Harsanyi support levels solutions, extend the Harsanyi solutions for LS-games. As an important subset of the class of these values, we present the class of weighted Shapley support levels values as a further result. The values from this class extend the weighted Shapley values for LS-games and contain the Shapley levels value as a special case. Axiomatizations of the studied classes are provided.

Due to the inevitability of nonlinear collisions between particles in ultracold atomic condensate experiments, it is of great significance to study the nonlinear effect for producing ultracold molecules from atomic condensates. In this work, we investigate theoretically the nonlinear effect induced by the two-body collision for producing ultracold Cs2 molecules from ultracold atoms by the stimulated Raman adiabatic passage in a tunneling four-level structure. Under the two-photon resonance condition and the coherent population trapping state, the conversion efficiency is influenced significantly by the nonlinear parameter. Meanwhile, the optimized parameter ranges of the resonance tunneling strength at the unstable excited molecular states, the effective Rabi frequencies of the two-laser fields, and the detuning of the pump field for different nonlinear parameters are suggested to obtain the high conversion efficiency of Cs2 molecules at the ground state. Finally, a maximum conversion efficiency of up to 88.56% can be realized in the optimized parameter ranges.

Рассматриваются некоторые характеристики сословной модели России в XVII - начале XX в. Основной особенностью социальной структуры России автор полагает наличие внутри каждого из сословий двух и более субсословий. Автор затрагивает также влияние этой характеристики на функционирование организационно-правового механизма вертикальной социальной мобильности. Some characteristics of the social class model of Russia in the 17th - early 20th centuries are considered. The author considers the presence of two or more sub-classes within each of the social class to be the main feature of Russian social structure. The author also touches upon the influence of this characteristic on the functioning of the organizational and legal mechanism of vertical social mobility.

We estimate the growth of cuspidal cohomology of G L 2 ( A Q ) . Quantitatively, we provide bounds on the total number of normalised eigenforms of Hecke operators which are obtained by automorphic induction from Hecke characters of imaginary quadratic fields grows as level structure varies. We further investigate how much of cuspidal cohomology of G L 3 ( A Q ) is obtained by symmetric square transfer from G L 2 ( A Q ) when the level structure corresponds to power of an odd prime.

The study of certain union $$X(\mu , b)$$ of affine Deligne–Lusztig varieties in the affine flag varieties arose from the study of Shimura varieties with Iwahori level structure. In this paper, we give an explicit dimension formula for $$X(\mu , b)$$ associated to sufficiently large dominant coweight $$\mu $$ .

Symmetries are known to play an important role in the low lying level structure of Sn isotopes, mostly in terms of the seniority and generalized seniority schemes. In this paper, we revisit the multi-j generalized seniority approach for the first excited $2^+$ and $3^-$ states in the Cd ($Z=48$), Sn ($Z=50$) and Te ($Z=52$) isotopes, where the Cd and Te isotopes represent two-proton hole and two-proton particle nuclei, thus involving both kind of particles (protons and neutrons) in contrast to Sn isotopes. Interestingly, the approach based on neutron valence space alone is able to explain the B(E2) and B(E3) trends respectively for the $2^+$ and $3^-$ states in all the three Cd, Sn and Te isotopes. The new results on the inverted parabolic behavior of B(E3) values in Cd and Te isotopes are understood in a manner identical to that of Sn isotopes by using the generalized seniority scheme. No shell quenching is supported by these calculations; hence, the neutron magic numbers, $N=50$ and $N=82$, remain robust in these isotopic chains. It is quite surprising that the generalized seniority continues to be reasonably successful away from the semi-magic region, thus providing a unifying view of the $2^+$ and $3^-$ states., Accepted in European Physical Journal Special Topics on role of symmetries in nuclear physics. arXiv admin note: substantial text overlap with arXiv:1908.05028

In this article, we describe the underlying reduced scheme of a quaternionic unitary Rapoport–Zink space with Iwahori level structure. In a previous work, we have studied the quaternionic unitary Rapoport–Zink space with a special maximal parahoric level structure. We will describe the morphism between these two Rapoport–Zink spaces and the fibers of this morphism. As an application of this result, we describe the quaternionic unitary Rapoport–Zink space with any parahoric level structure.

We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local models attached to all connected reductive groups over $p$-adic local fields with $p\geq 5$. In addition, we give a self-contained study of relative affine Grassmannians and loop groups formed using general relative effective Cartier divisors in a relative curve over an arbitrary Noetherian affine scheme., Minor corrections; added {\S}{\S}7-8 on the test function conjecture for modified local models

Topical issues of the structure and evaluation of the volume of the international space market, as well as the efficiency of enterprise activity in the rocket and space industry are considered. A five-level value chain model of the space market is proposed (“products”–“infrastructure”–“services”–“factors in the formation of public goods”). It was shown that the application of various approaches to eliminating double counting arising from the addition of volumes of product deliveries “inside” the rocket and space industry and deliveries of products and services to end users, where these “internal” deliveries are included in the cost of the corresponding operator, can lead to a discrepancy in estimating market volume by more than one and a half times. It has been demonstrated that the use of the added value estimation considering purchasing power parity leads to a convergence of labor productivity estimates in the domestic and foreign rocket and space industries (50–60% of the corresponding indices for the US and German space industries). The expediency of further studies aimed at transferring from a model implementation of the proposed approaches to the formation of a full segmented estimation of the international space market (ISM) based on added cost is determined.

A survey of experimental results on the level structure in the heavy helium isotope $${}^{6}$$ He that were obtained in reactions induced by stopped pion absorption in $${}^{9}$$ Be, $${}^{10,11}$$ B, and $${}^{12}$$ C light nuclei is presented. The respective measurements were performed on the low-energy pion channel of the accelerator at the Los Alamos National Laboratory (LANL) by means of a two-arm semiconductor spectrometer. A high statistical significance of the results was attained over a broad excitation-energy range extending up to 40 MeV. Several highly excited states, including $$t+t$$ cluster resonances, were revealed for the first time.

Shell model calculations have been carried out for 90Nb nucleus with the model space in which the valence protons occupy the f5/2, p3/2, p1/2, and g9/2 orbitals and the valence neutrons occupy the p1/2, g9/2, d5/2, and g7/2 orbitals. According to the calculated results, the negative parity is from the contribution of the proton of the f5/2, p3/2, and p1/2 orbits. The moderate spin states of 90Nb are mainly due to the excitation of protons from the f5/2 and p3/2 orbits to the p1/2 and g9/2 orbits across the Z = 38 subshell closure, and the high spin states arise from the excitation of a single neutron from the g9/2 orbit into the d5/2 orbit across the N = 50 shell closure.

The low-lying excited states in the neutron-deficient $N = Z + 1$ nucleus $^{87}_{43}$Tc$_{44}$ have been studied via the fusion-evaporation reaction $^{54}$Fe $(^{36}Ar, 2n1p)$ $^{87}$Tc at the Grand Accelerateur National d'Ions Lourds (GANIL), France. The AGATA spectrometer was used in conjunction with the auxiliary NEDA, Neutron Wall, and DIAMANT detector arrays to measure coincident prompt γ rays, neutrons, and charged particles emitted in the reaction. A level scheme of $^{87}$Tc from the $(9/2^+_{g.s})$ state to the $( 33 / 2^+_1$) state was established based on six mutually coincident γ -ray transitions. The constructed level structure exhibits a rotational behavior with a sharp backbending at $ℏω ≈ 0.50$ MeV. A decrease in alignment frequency and increase in alignment sharpness in the odd-mass isotonic chains around $N=44$ is proposed as an effect of the enhanced isoscalar neutron-proton interactions in odd-mass nuclei when approaching the $N=Z$ line.

Low-lying states of Cd-98 have been populated by the two-nucleon removal reaction (In-100, Cd-98+gamma) and studied using in-beam gamma-ray spectroscopy at the Radioactive Isotope Beam Factory at RIKEN. Two new gamma transitions were identified and assigned as decays from a previously unknown state. This state is suggested to be based on a pi 1g(/9/2)(-1)2p(1/2)(-2) configuration with J(pi) = 5(-). The present observation extends the systematics of the excitation energies of the first 5(-) state in N = 50 isotones toward Sn-100. The determined energy of the 5(- )state in Cd-98 continues a smooth trend along the N = 50 isotones. The systematics are compared with shell-model calculations in different model spaces. Good agreement is achieved when considering a model space consisting of the pi(1f(5/2), 2p(3/2), 2p(1/2), 1g(9/2)) orbitals. The calculations with a smaller model space omitting the orbitals below the Z = 38 subshell could not reproduce the experimental energy difference between the ground and first 5(-) states in N = 50 isotones, because proton excitations across Z = 38 subshell yield a large amount of correlation energy that lowers the ground states. (Less)

In order to research the multi-level structure of Lyocell fiber at different draw ratios and to reveal the limiting factors for preparing the high strength Lyocell fiber, the paper reports on the effect of draw ratio including low drawing (1–5), high drawing (6–11) and excessive drawing (12–20) on the multi-level structure and the mechanical properties of Lyocell fiber. The structure was determined by wide-angle X-ray diffraction, small-angle X-ray scattering and fibrillation test, and the result showed that, at low draw ratio stage, the breaking strength, yield strength and modulus of the fiber increased with the draw ratio owing to crystallinity as well as orientation increased while the micropore decreased, and there are almost no microfibrils on the fiber surface. At high draw ratio stage, the orientation of amorphous region increasing was the principal reason for the increase of fiber mechanical properties, and the micropores continued to decrease and a few short and thick microfibril was formed. At excessive draw ratio stage, the breaking strength remained constant mainly due to the basically unchanged crystallinity and orientation of the fibers, the yield strength and modulus decreased due to the slip of the highly crystallized and oriented elementary fibril. Meanwhile, the micropores still decreased and became much slenderer, the number of microfibrils increased and the microfibrils showed tenuous structure. It could be summarized that Lyocell fiber had the characteristics of multi-level structure, and the fundamental reason limiting the improvement of mechanical properties with draw ratio increase was the slip of elementary fibril.

Electric dipole spin resonance (EDSR) is a commonly used tool for manipulation and spectroscopy of quantum-dot-based spin qubits. When an EDSR experiment is embedded in a transport setup and Pauli spin blockade is used as means for spin-state read-out, then measured resonant responses in the leakage current indeed carry information about the level structure of the system under study. However, the actual line shape of these current resonances differs substantially from experiment to experiment, varying from being symmetric to asymmetric and from being a peak to a dip, a thorough understanding of which is still lacking. Here, we investigate theoretically the detailed line shape of EDSR-induced resonances in the leakage current in the regime of spin blockade, and we connect different line shapes to the different underlying physical mechanisms that can enable the EDSR. We carry out both numerical and analytical investigations, producing simple analytic expressions that give insight in the physics at play. Our results thus provide a means to extract more information about the detailed system parameters of quantum dots hosting spin qubits from an EDSR experiment than just their level structure based on the location of the resonances., 13 pages, 9 figures, two appendices

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH 5 +based on the motion of an effective particle confined to a 60-vertex graphΓ 60with a single edge length parameter. Within this model, the quantum states of CH 5 +are obtained in analytic form and are related to combinatorial properties ofΓ 60. The bipartite structure ofΓ 60gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH 5 +

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk bandstructure of silicon, which has six degenerate electronic minima. The degeneracy can be lifted in silicon quantum wells due to strain and electronic confinement, but the "valley splitting" of the two lowest lying valleys is known to be sensitive to atomic-scale disorder. Large valley splittings are desirable to have a well-defined spin qubit. In addition, an understanding of the inter-valley tunnel coupling that couples different valleys in adjacent quantum dots is extremely important, as the resulting gaps in the energy level diagram may affect the fidelity of charge and spin transfer protocols in silicon quantum dot arrays. Here we use microwave spectroscopy to probe spatial variations in the valley splitting, and the intra- and inter-valley tunnel couplings ($t_{ij}$ and $t'_{ij}$) that couple dots $i$ and $j$ in a triple quantum dot (TQD). We uncover large spatial variations in the ratio of inter-valley to intra-valley tunnel couplings $t_{12}'/t_{12}=0.90$ and $t_{23}'/t_{23}=0.56$. By tuning the interdot tunnel barrier we also show that $t'_{ij}$ scales linearly with $t_{ij}$, as expected from theory. The results indicate strong interactions between different valley states on neighboring dots, which we attribute to local inhomogeneities in the silicon quantum well.

The hot nucleus $^{171}\mathrm{Yb}$ is investigated by the covariant density functional theory with the PC-PK1 effective interaction. The thermodynamic quantities are evaluated with the canonical ensemble theory. The pairing correlations is treated by the shell-model-like approach, in which the particle numbers are conserved strictly and in which the blocking effect is handled exactly. An S-shaped heat capacity versus temperature of $^{171}\mathrm{Yb}$ appears. It has been studied in terms of the blocking effect, the single-particle levels, the pairing gap, and defined seniority components, and compared to the heat capacity of $^{172}\mathrm{Yb}$. The pairing transition from the superfluid state to the normal state can result in the S-shaped heat capacity of $^{172}\mathrm{Yb}$ where the one-pair-broken and two-pair-broken states dominate, while the single-particle level structure near the Fermi surface is associated with the S-shaped heat capacity of $^{171}\mathrm{Yb}$. For odd-$A$ nuclei, although the one-pair-broken and two-pair-broken states still contribute, the pairing gap and the pairing transition is relatively weak. The S-shaped heat capacity could be affected due to the blocking of the single-particle level near the Fermi surface.

A new critical point symmetry (CPS) for odd-even systems is developed through coupling the T(4) CPS to a single particle within a spherical-j orbit. The resulting model is shown to be exactly solvable and serve as the triaxial CPS for transitional odd-A nuclei. A comparison between the model calculations and the available data on 135Ba indicates that the new CPS model at a large-γ deformation in the case of j = 3 / 2 may yield the dynamical predictions being very similar to those from the E(5/4) CPS, thus providing an alternative explanation of the level structure built on the single-particle orbit 2 d 3 / 2 in 135Ba.