Scattering theory for lattice operators in dimension d≥3d\geq 3

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension $d\geq 3$ the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in presence of embedded eigenvalues and threshold singularities.Comment: Minor errors and misprints corrected; new result on absense of embedded eigenvalues for potential scattering; to appear in RM

On transversally elliptic operators and the quantization of manifolds with ff-structure

An $f$-structure on a manifold $M$ is an endomorphism field \phi\in\Gamma(M,\End(TM)) such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure E_{1,0}\subset T_\C M given by the $+i$-eigenbundle of $\phi$. Using a compatible metric $g$ and connection $\nabla$ on $M$, we construct an odd first-order differential operator $D$, acting on sections of $\S=\Lambda E_{0,1}^*$, whose principal symbol is of the type considered in arXiv:0810.0338. In the special case of a CR-integrable almost $\S$-structure, we show that when $\nabla$ is the generalized Tanaka-Webster connection of Lotta and Pastore, the operator $D$ is given by D = \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann operator. We then describe two "quantizations" of manifolds with $f$-structure that reduce to familiar methods in symplectic geometry in the case that $\phi$ is a compatible almost complex structure, and to the contact quantization defined in \cite{F4} when $\phi$ comes from a contact metric structure. The first is an index-theoretic approach involving the operator $D$; for certain group actions $D$ will be transversally elliptic, and using the results in arXiv:0810.0338, we can give a Riemann-Roch type formula for its index. The second approach uses an analogue of the polarized sections of a prequantum line bundle, with a CR structure playing the role of a complex polarization.Comment: 31 page

Overtwisted energy-minimizing curl eigenfields

We consider energy-minimizing divergence-free eigenfields of the curl operator in dimension three from the perspective of contact topology. We give a negative answer to a question of Etnyre and the first author by constructing curl eigenfields which minimize $L^2$ energy on their co-adjoint orbit, yet are orthogonal to an overtwisted contact structure. We conjecture that $K$-contact structures on $S^1$-bundles always define tight minimizers, and prove a partial result in this direction.Comment: published versio

Eficienta economică şi tehnologică a utilizării giberelinei la soiurile pentru struguri de masă

iticulture for the agriculture of Moldova is an important and effective branch, but the table grapes sector is an efficient and more important for small, medium and family business. Increasing the quality of table grapes is a necessity for society and consumers. The purpose of the research from this article is to study the influence of Gobbi Gib 2LG on the quantity, quality and economic efficiency of grapes of Beauty Seedless and Prezentabil varieties. The research was conducted in the vineyards of the „Terra Vitis” LTd, from Southern wine region in Moldova. Research results have shown that the dose of 2.4 l/ha is most useful for conditions by the south part of Moldova, for Beauty seedless variety and the dose of 0,98 l/ha for Prezentabil varieti

Special biconformal changes of K\"ahler surface metrics

The term "special biconformal change" refers, basically, to the situation where a given nontrivial real-holomorphic vector field on a complex manifold is a gradient relative to two K\"ahler metrics, and, simultaneously, an eigenvector of one of the metrics treated, with the aid of the other, as an endomorphism of the tangent bundle. A special biconformal change is called nontrivial if the two metrics are not each other's constant multiples. For instance, according to a 1995 result of LeBrun, a nontrivial special biconformal change exists for the conformally-Einstein K\"ahler metric on the two-point blow-up of the complex projective plane, recently discovered by Chen, LeBrun and Weber; the real-holomorphic vector field involved is the gradient of its scalar curvature. The present paper establishes the existence of nontrivial special biconformal changes for some canonical metrics on Del Pezzo surfaces, viz. K\"ahler-Einstein metrics (when a nontrivial holomorphic vector field exists), non-Einstein K\"ahler-Ricci solitons, and K\"ahler metrics admitting nonconstant Killing potentials with geodesic gradients.Comment: 16 page

Tight Beltrami fields with symmetry

Let $M$ be a compact orientable Seifered fibered 3-manifold without a boundary, and $\alpha$ an $S^1$-invariant contact form on $M$. In a suitable adapted Riemannian metric to $\alpha$, we provide a bound for the volume $\text{Vol}(M)$ and the curvature, which implies the universal tightness of the contact structure $\xi=\ker\alpha$.Comment: 26 page

Comparative Study Between Solid State Welding and Radiant Energy Welding Processes for Joining Metallic Glassy Ribbons

Amorphous alloys have emerged as an important class of advanced materials that own a combination of properties, such as mechanical strength, hardness, high elasticity modulus and a very good corrosion resistance. Since the number of amorphous structures alloys increased in the last decades, ways of joining such materials were studied in order to produce complex structures or increase their size. Thus, if this kind of complex products are obtained, it will diversify their applicability in multiple and various domains. For this research two ways of joining amorphous ribbons has been studied: solid state welding and radiant energy welding. For the radiant energy welding process, it was selected electron beam welding (EBW) method and for the solid-state welding process, ultrasonic welding (UW) method was chosen. Seeing that these methods have found applicability in industries, a comparative study was done in order to see which one offers the best outcome. Recently, in the last years, such products were embedded in a polymer matrix, creating thus, composite materials that have improved mechanical properties. This raised curiosity for major industries, such as aero-space, medical and automotive. Amorphous ribbons from Ni-Fe-Cr-Si-B and Al-Ni-Nd-Co alloy families were welded by EBW method, and Cu-Zr-Al amorphous ribbons were welded by the UW method. Microstructure characterization has been performed by SEM, EDX, XRD and DSC analyses

Once more on the Witten index of 3d supersymmetric YM-CS theory

The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.Comment: 27 page

Spherical nucleic acids as an infectious disease vaccine platform

Despite recent efforts demonstrating that organization and presentation of vaccine components are just as important as composition in dictating vaccine efficacy, antiviral vaccines have long focused solely on the identification of the immunological target. Herein, we describe a study aimed at exploring how vaccine component presentation in the context of spherical nucleic acids (SNAs) can be used to elicit and maximize an antiviral response. Using COVID-19 as a topical example of an infectious disease with an urgent need for rapid vaccine development, we designed an antiviral SNA vaccine, encapsulating the receptor-binding domain (RBD) subunit into a liposome and decorating the core with a dense shell of CpG motif toll-like receptor 9 agonist oligonucleotides. This vaccine induces memory B cell formation in human cells, and in vivo administration into mice generates robust binding and neutralizing antibody titers. Moreover, the SNA vaccine outperforms multiple simple mixtures incorporating clinically employed adjuvants. Through modular changes to SNA structure, we uncover key relationships and proteomic insights between adjuvant and antigen ratios, concepts potentially translatable across vaccine platforms and disease models. Importantly, when humanized ACE2 transgenic mice were challenged in vivo against a lethal live virus, only mice that received the SNA vaccine had a 100% survival rate and lungs that were clear of virus by plaque analysis. This work underscores the potential for SNAs to be implemented as an easily adaptable and generalizable platform to fight infectious disease and demonstrates the importance of structure and presentation in the design of next-generation antiviral vaccines

Noble gas and carbon isotope systematics at the seemingly inactive Ciomadul volcano (Eastern‐Central Europe, Romania): evidence for volcanic degassing

Ciomadul is the youngest volcano in the Carpathian-Pannonian Region, Eastern-Central Europe, which last erupted 30 ka. This volcano is considered to be inactive, however, combined evidence from petrologic and magnetotelluric data, as well as seismic tomography studies suggest the existence of a subvolcanic crystal mush with variable melt content. The volcanic area is characterized by high CO2 gas output rate, with a minimum of 8.7 × 103 t yr-1. We investigated 31 gas emissions at Ciomadul to constrain the origin of the volatiles. The δ13C-CO2 and 3He/4He compositions suggest the outgassing of a significant component of mantle-derived fluids. The He isotope signature in the outgassing fluids (up to 3.10 Ra) is lower than the values in the peridotite xenoliths of the nearby alkaline basalt volcanic field (R/Ra 5.95Ra±0.01) which are representative of a continental lithospheric mantle and significantly lower than MORB values. Considering the chemical characteristics of the Ciomadul dacite, including trace element and Sr- Nd and O isotope compositions, an upper crustal contamination is less probable, whereas the primary magmas could have been derived from an enriched mantle source. The low He isotopic ratios could indicate a strongly metasomatized mantle lithosphere. This could be due to infiltration of subduction-related fluids and postmetasomatic ingrowth of radiogenic He. The metasomatic fluids are inferred to have contained subducted carbonate material resulting in a heavier carbon isotope composition (13C is in the range of -1.4 to -4.6 ‰) and an increase of CO2/3He ratio. Our study shows the magmatic contribution to the emitted gases