Exponential Factor Research Articles

Factorization of holomorphic matrices and Kazhdan's property (T)

In this article we deduce some algebraic properties for the group Sp2n(O(X)) of holomorphic symplectic matrices on a Stein space X: holomorphic factorization, exponential factorization, and Kazhdan's property (T). In holomorphic factorization we combine a recent result of the third author and K-theory tools to give explicit bounds for the case when X is one-dimensional or two-dimensional. Next we use them to find bounds for exponential factorization. As a further application, we show that the elementary symplectic group Ep2n(O(X)) admits Kazhdan's property (T).

Evaluation of Saturation Interpretation Methods for Ultra-Low Permeability Argillaceous Sandstone Gas Reservoirs: A Case Study of the Huangliu Formation in the Dongfang Area

Ultra-low permeability argillaceous sandstone reservoirs have become a significant focus for exploration and development. Saturation is a crucial parameter in evaluating such reservoirs. Due to the low porosity, low permeability, complex pore structure, and strong heterogeneity in ultra-low permeability argillaceous sandstone reservoirs, traditional evaluation methods are unable to achieve the required level of interpretation accuracy. To improve the accuracy of gas saturation calculations in ultra-low permeability argillaceous sandstone gas reservoirs, the conductivity characteristics of the ultra-low permeability argillaceous sandstone gas reservoirs in the Huangliu Formation in the Dongfang area, China, were analyzed through rock physics experimental data and geological information. The results revealed the clay content in the study area to range from 6% to 33.4%. Influenced by burial depth and temperature, kaolinite and montmorillonite transform into illite and chlorite, and the cation exchange capacity is not correlated with the clay content. This suggests that the effects of cation-attached conductivity can be ignored. The regional variation in rock electrical parameters is significant. When the lithology coefficient is a = 1, the consolidation index m varies between 1.25 and 1.75. When the lithology coefficient is b = 1, the saturation index n varies between 1.6 and 1.96. Under the influence of high temperature and pressure, the reservoirs in the study area exhibit two distinct characteristics on the capillary pressure curve, fractal dimension, and effective porosity index intersection diagram, (1) In Class I reservoirs, there is a strong correlation between the formation factor and natural gamma, as well as porosity, and a logarithmic relationship between the saturation exponent and the formation factor; and (2) in Class II reservoirs, there is a strong power-law relationship between the formation factor and porosity, as well as a logarithmic relationship between the saturation exponent and formation factor. Based on experimental and logging data, reservoir classification was conducted using core-scale logging and principal component analysis. Additionally, a saturation interpretation model was developed using multivariate regression, based on rock electrical parameters. The actual application results demonstrate that compared to the fixed rock resistivity saturation model, this model has reduced the average absolute error by 5.9%. The calculated values are consistent with the gas saturation analysis of the core at the pure gas section as determined by cable testing sampling. This model meets the requirements of practical production. The study of this interpretation method is of great significance for the formulation of development plans for ultra-low permeability offshore argillaceous sandstone gas reservoirs.

The bitumen development effect on the pore structure and electrical resistivity of carbonate reservoirs in the Sinian Dengying Formation

Abstract In the Sichuan Basin, bitumen widely distributes in the carbonate reservoir, and the bitumen occurrence morphology affects the pore structure and petrophysics. Two types of bitumen, boundary-filled and centre-filled, were reconstructed using a pore morphology-based method based on dolomite carbonate digital cores from X-ray computerized tomography. The pore structures of the reconstructed bitumen-filled digital core models were determined using an extracted pore network model. The finite element method simulated the electrical resistivity of the digital core model. The investigation showed that (i) boundary-developed bitumen increases the pore size whereas centre-developed bitumen decreases the pore size, and bitumen development increases the shape factor while reducing the coordination number; (ii) for electrical resistivity, boundary-filled bitumen increases the porosity exponent with increasing pore size, whereas centre-filled bitumen decreases the porosity exponent. Bitumen development caused a negative correlation between the porosity exponent and pore shape factor, a logarithmic increase between the porosity exponent and coordination number, and a power increase between the porosity exponent and porosity. Subsequently, a new porosity exponent model related to porosity was proposed based on the curve-fitting method. This new porosity exponent combines the Archie equations to calculate the saturation of the carbonate reservoir in the Sinian Dengying Formation in the Penglai gas area on the northern slope of the central Sichuan paleo-uplift, which fits the sealed core plug saturation well and provides the basis for further reservoir evaluation and fluid identification in the Penglai gas area.

Study of Nonlinear Evolution of Spacetime Fluctuations in Quantum Gravity Inflation for Deriving Primordial Spectrum

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about 1017 GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology.

Moving-Target Circumnavigation Using Adaptive Neural Anti-Synchronization Control via Distance-Only Measurements.

In this work, we investigate the unknown moving-target circumnavigation problem in GPS-denied environments. A minimum of two tasking agents is excepted to circumnavigate the target cooperatively and symmetrically without prior knowledge of its position and velocity in order to achieve optimal sensor coverage persistently for the target. To achieve this goal, we develop a novel adaptive neural anti-synchronization (AS) controller. Based on relative distance-only measurements between the target and two tasking agents, a neural network is used to approximate the displacement of the target such that the position of the target can be estimated accurately and in real time. On this basis, a target position estimator is designed by considering whether all agents are in the same coordinate system. Furthermore, an exponential forgetting factor and a new information utilization factor are introduced to improve the accuracy of the aforementioned estimator. Rigorous convergence analysis of position estimation errors and AS error shows that the closed-loop system is globally exponentially bounded by the designed estimator and controller. Both numerical and simulation experiments are conducted to demonstrate the correctness and effectiveness of the proposed method.

Towards Online Data-Driven Discovery of Autonomous Ship Models for Digital Twins

In this paper, we introduce a novel approach for discovering governing equations of autonomous ships from data, intended for integration into digital twins. Our method relies on an online adaptive observer comprising two interconnected exponential forgetting factor designs, one for the state and another for the parameters. With sufficient persistency of excitation, our method accurately identifies the underlying models. Numerical simulations demonstrate the effectiveness of our proposed approach, highlighting its potential for practical application in the development of digital twins for autonomous ships. The adaptive observer's dual design, for both state and parameter considerations, enhances its adaptability and robustness, making it a promising tool for accurate model discovery.

Characterization of NTC thick film thermistor paste Cu0.2Ni0.5Zn1.0Mn1.3O4

A powder of Cu0.2Ni0.5Zn1.0 Mn1.3O4 composition for custom thermistor was prepared by using the respective mixture of metal oxides and solid state reaction at 1000 ?C/4h in air. The obtained thermistor powder was milled in the planetary ball mill and agate mill for a prolonged time to achieve submicron powder. The prepared thermistor powder was further characterized by using XRD and SEM techniques. After that, the thermistor powder was pressed into small disc-shaped samples and sintered at 1150?C/2h. The sintered samples were also characterized by using XRD and SEM. The main electrical properties such as nominal resistance R and thermistor exponential factor B were measured in the climatic test chamber. After that, the thick film paste was prepared using the same powder, an organic vehicle and a glass frit. The paste was printed on alumina substrate, dried at 150 =?C /30 min and sintered in air at 850?C /10 min in a hybrid conveyor furnace. Planar electrodes were printed on the sintered NTC thermistor layer using PdAg thick film paste. The electric properties of the sintered thick film thermistor were also measured in the climatic test chamber. The obtained results were used for development of novel self-heating thermistor applications.

Forecasting hourly WTI oil front monthly price volatility densities

<p>Financial commodity markets have an impact on company values and cash flows, where price movements within frequent time intervals can be both significant and random. Understanding highly frequent price movements is both important and difficult. In this paper, I measured and forecasted volatility for high-frequency (mostly twelve hours per day) WTI Oil front month price movements from 2012 to 2024 (about 40,500 observations). I created a new stochastic volatility model for extracting latent volatility using the non-linear Kalman filter. Stable and strictly ergodic hourly price series, along with the BIC optimal non-linear (generic) general method of moments model coefficients, enabled this process. The latent volatility seemed to separate into two volatility factors. One factor that was very persistent suggested slow mean reversion, and one choppy strongly mean-reverting factor. The data dependence found in the factor volatility series suggested forecasting ability. I applied classical static forecasts and three machine learning regression techniques to predict one-step-ahead volatility. The two volatility factors and one summarizing exponential factor were reported, along with several fit measures, including the root mean square error and Theil's measure of covariance.</p>

Investigation of wind veer characteristics on complex terrain using ground-based lidar

The wind direction shift with height significantly influences wind turbine performance, particularly in relation to terrain conditions. In this work, wind conditions at 12 measurement heights ranging from 40 m to 200 m using a ground lidar, Windcube V2, installed on a 16 m tall building were analysed to examine the characteristics of wind veer angles in complex terrain. The measurement campaign was carried out from January 1st to December 31st, 2022, in the southeastern part of South Korea. The terrain complexity around the ground lidar system was evaluated using the ruggedness index (RIX), whose result was 14.06 percent corresponding to complex terrain. The ground lidar measurements were compared with mesoscale data, EMD-WRF South Korea, for the data accuracy check. Wind veer frequencies and wind roses were derived to identify directional shifts with height. Furthermore, diurnal, monthly, and seasonal variations of wind veer characteristics were analysed. Wind shear exponent factor (WSE) and turbulence kinetic energy (TKE) were calculated, and wind veer profiles were constructed based on these parameters. The relative errors of wind speeds were analysed for rotor equivalent wind speed (REWS) and hub height wind speed (HHWS), with REWS with wind veer correction, REWSveer, as a reference. Additionally, atmospheric stability conditions were classified using WSE and TKE, and the vertical changes in wind veering were analysed according to the stability conditions. The findings reveal lower wind speeds exhibited larger wind veer values and fluctuations. The relative errors for the REWS and the HHWS were 0.04 % and 0.20 % on average, respectively. The study demonstrates that terrain conditions significantly impacted wind veer angles at heights below 100 m, whereas the influence diminished with increasing height above 100 m. The results could be helpful for wind farm developers to make decisions on the siting as well as the hub height of wind turbines on complex terrain

Bianchi Type V Cosmological Scenario In f(R,T) Gravity Theory With Special Form Of Scale Factor

In this study, we have examined the exact solutions of the field equations for a Bianchi type V universe filled with bulk viscous fluid within the framework of theory, where and and represent the Ricci scalar and the trace of the energy momentum tensor, respectively. We used a combination of exponential and hyperbolic scale factors to determine the physical parameters and metric potentials in the space-time. We also investigated the geometrical and physical parameters of the model, as well as the energy conditions. Additionally, we found that the state finder diagnostic pair falls within an acceptable range.

Scattering on self-dual Taub-NUT

We derive exact solutions of massless free field equations and tree-level two-point amplitudes up to spin 2 on self-dual Taub-NUT (SDTN) spacetime, as well as on its single copy, the self-dual dyon (SDD). We use Killing spinors to build analogues of momentum eigenstates, finding that, in the spirit of color-kinematics duality, those for the SDD lift directly to provide states on the SDTN background if one replaces charge with energy. We discover that they are forced to have faster growth at infinity than in flat space due to the topological non-triviality of these backgrounds. The amplitudes for massless scalars and spinning particles in the and helicity configurations vanish for generic kinematics as a consequence of the integrability of the self-dual sector. The amplitudes are non-vanishing and we compute them exactly in the backgrounds, which are treated non-perturbatively. It is explained how spin is easily introduced via a Newman–Janis imaginary shift along the spin-vector leading directly to the well-known exponential factor in the dot product of the spin with the momenta. We also observe a double copy relation between the gluon amplitude on a SDD and graviton amplitude on a SDTN spacetime.

An optimum design of a ring Airyprime beam array based on dimensionless eccentric position

The beam array with abruptly autofocusing capability weakens the turbulence effect in free space optical (FSO) communication systems with relatively low complexity, thereby improving the communication quality of FSO communication systems. Based on the perspective of dimensionless eccentric position B, the design of a ring Airyprime beam array (RAPBA) is optimized to achieve the strongest autofocusing capability. When B increases from zero, the autofocusing capability of a RAPBA first increases, then reaches a maximum value, and finally decreases. With given the exponential decay factor a, an optimum value of B under which the autofocusing capability is the strongest is searched out. With the decrease of a, the optimum value of B increases. When a = 0.05, the autofocusing capability of a RAPBA with the optimum B is enhanced by 373.66 % compared with the maximum autofocusing capability of a circular Airyprime beam, while the corresponding focal length is only shortened by 4.73 %. Also, we construct a concise experimental optical setup for the acquisition and the measurement of a RAPBA. The measured results support the theoretical predictions. The physical logical principles underlying the autofocusing capability and the dimensionless eccentric position is interpreted. This research offers a novel approach for an optimum design of a RAPBA with the strongest autofocusing capability. A similar variation pattern of autofocusing capability and dimensionless eccentric position exists in a ring Airy beam array (RABA). Accordingly, our proposed scheme is also suitable for the optimum design of a RABA.

Tuning exponential decay factor in oligophenylene molecular junctions with graphene nanoribbon electrodes

We explore the transport properties of oligophenylene molecular junctions, where the center molecule containing 1, 2, or 3 phenyls is sand-wiched between two graphene nanoribbons (GNR) with different edge shapes. According to the obtained results of the first-principles calculations combined with non-equilibrium Green’s function method, we find that the molecular length-dependent resistance of all examined oligophenylene molecular junctions follows well the exponential decay law with different slopes, and the exponential decay factor is sensitive to the edge shape of GNRs and the molecule-electrode connecting configuration. These observations indicate that the current through the oligophenylene molecular junction can be effectively tuned by changing the edge shape of GNRs, the molecular length, and the molecular contacting configuration. These findings provide theoretical insight into the design of molecular devices using GNRs as electrodes.

Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System

A theoretically and numerically analysis on Duffing Jerk systems with a sixth-order type potential and a sixth-order potential smoothed by a gaussian function are carried out in this work. The Jerk is transformed into a dynamical system of dimension three. The dynamics and stability of the resulting system are analyzed, through phase space, bifurcation diagrams and Lyapunov exponents by varying the relevant parameters, finding the existence of a strange attractor. The dynamics of system with potential smoothed was studied by varying the smoothing parameter $\alpha$, finding that this parameter can be used to controlling chaos, since the exponential factor keeps the same fixed points and it regulates smoothly the amplitude of the potential.

Calorimetric studies of yttrium doped non-conventional phase-change materials for improved performance

Though phase-change materials (PCMs) are regarded as constituent part of next-generation phase-change memory and other unfolding optoelectronic applications, the kinetics study of glass transition and crystallization, significant property in switching remains obscure in high-temperature region. Hence, this paper reports the investigation of glass transition and crystallization kinetics of Te(1-x) (GeSe0.5)Yx (TGSY) chalcogenide glass using differential scanning calorimetry (DSC) at heating rates 5, 10, 15, 20 °C/min. The effect of increasing Y quantity has been described by connecting structural relaxation kinematics during glass transition phenomena and devitrification while crystallization in chalcogenide glasses with their varied physicochemical characteristics. The inclusion of Y causes a discernible rise in the crystallization rate. The system is compatible with a strong glass-forming liquid, according to the Te(1-x) (GeSe0.5) Yx material fragility index. According to the average values of the kinetic exponent factors, there is heterogeneous nucleation for the investigated composition, which is subsequently followed by a two- or three-dimensional crystal growth phenomenon. Different glass stability criteria have been discussed based on the relationship between the characteristic temperatures. The CZW and CLX criteria were found to be inappropriate for discussing glass stability (GS) for the studied compositions based on the heating rate and composition dependencies of all criteria. The CYL criteria of Yuan et al. is the finest and it demonstrates the optimal ability for evaluating the GS, according to the data that was extracted from several GS criteria and their relative change parameters. By adding Y, thermal stability parameter and enthalpy emitted during the transition of glass and crystalline phases have been found to have an inverse relationship. All studied properties can conclude the application of studied material in phase-change material devices.

Climate change and infectious disease surveillance in Nepal: qualitative study exploring social, cultural, political and institutional factors influencing disease surveillance.

To explore the impacts of contextual issues encompassing social, cultural, political and institutional elements, on the operation of public health surveillance systems in Nepal concerning the monitoring of infectious diseases in the face of a changing climate. Semi-structured interviews (n=16) were conducted amongst key informants from the Department of Health Services, Health Information Management System, Department of Hydrology and Meteorology, World Health Organization, and experts working on infectious disease and climate change in Nepal, and data were analysed using thematic analysis technique. Analysis explicates how climate change is constructed as a contingent risk for infectious diseases transmission and public health systems, and treated less seriously than other 'salient' public health risks, having implications for how resources are allocated. Further, analysis suggests a weak alliance among different stakeholders, particularly policy makers and evidence generators, resulting in the continuation of traditional practices of infectious diseases surveillance without consideration of the impacts of climate change. We argue that along with strengthening systemic issues (epidemiological capacity, data quality and inter-sectoral collaboration), it is necessary to build a stronger political commitment to urgently address the influence of climate change as a present and exponential risk factor in the spread of infectious disease in Nepal.

Temperature dependent magnetic and electrical transport properties of lanthanum and samarium substituted nanocrystalline nickel ferrite and their hyperthermia applications

Structural, optical, temperature dependent magnetic and electrical properties have been investigated for the nanocrystalline NiFe1.97RE0.03O4 (RE = La3+ and Sm3+) compound. Without any signs of a secondary REFeO3 phase, the Rietveld refinement reveals a single-phase spinel structure possessing cubic symmetry for current samples. The decrease in lattice constant has been observed as a result of RE ions substitution. The TEM micrographs reveal nanosized particles with an average size of 35 ± 3 nm and 32 ± 3 nm for La3+ and Sm3+ substituted samples. EDX spectra of both samples show good compositional homogeneity. HRTEM micrographs of both samples show well resolved lattice fringes and their inter-planar spacing matches with that obtained from the Rietveld analysis of the XRD patterns. The concentration of Fe2+ and Fe3+ ions has been estimated from the XPS spectra analysis and it is found to be ∼ 22% and 78% for NiFe1.97La0.03O4 and, 20% and 80% for NiFe1.97Sm0.03O4 compound. The optical energy band gap for rare earth substituted samples is found to be more than that of pure nickel ferrite. The value of saturation magnetization (Ms) and magneto-crystalline anisotropy constant (K1) estimated from the “Law of Approach to Saturation” equation for rare earth substituted samples are found to be less than that of pure nickel ferrite. However, an enhanced value of coercivity has been observed with RE substitution. ZFC (zero field cooling) and FC (field cooling) DC magnetization curves measured at 100 Oe in the temperature range of 60–400 K reveal a combination of weak and intermediate forms of magnetic interaction between the particles for both samples. Temperature dependent analysis of saturation magnetization and coercivity employing modified Bloch’s law and Kneller’s relation supports the nanomagnetic behavior of both samples. Under an AC magnetic field of 14.92 kA/m and frequency 337 kHz, the SAR and ILP values have been found to be ∼ 331 W/g and 4.22 nHm2/kg for NiFe1.97La0.03O4 and, ∼ 241 W/g and 3.21 nHm2/kg for NiFe1.97Sm0.03O4. The dielectric relaxation data have been analyzed at various temperatures ranging from 40 to 300 0C over the frequency range 100 Hz-1 MHz using electrical impedance spectroscopy. The dielectric constant for rare earth substituted samples is found to be more and their AC conductivity is observed to be less than that of pure nickel ferrite. The analysis of temperature dependent AC conductivity employing Jonscher’s power law suggests that the charge carrier’s conduction mechanism of both samples follows the small polaron hopping mechanism below 200 0C, thereafter; it follows the correlated barrier hopping mechanism. The activation energy estimated by imaginary impedance spectra is found to be 0.411 eV and 0.398 eV for NiFe1.97La0.03O4 and NiFe1.97Sm0.03O4 which is more than that of pure nickel ferrite. The Cole-Cole plots at different temperatures suggest the presence of non-Debye-type relaxation. The modeling of Cole-Cole plots with equivalent circuits for both samples confirms the contribution of both grain and grain boundary in electrical conduction. The estimated stretching exponential factor by fitting the modified KWW (Kohlrausch-Williams-Watts) equation to the imaginary modulus curve reveals relatively more dipole-dipole interaction in NiFe1.97Sm0.03O4 than that of the La3+ substituted sample.

Influence of exponential heat source, variable viscosity and shape factor on a hybrid nanofluid flow over a flat plate when thermal radiation and chemical reaction are significant

The significance of hybrid nanofluid flow over a flat plate lies in its ability to enhance heat transfer, improve energy efficiency, enable temperature control, and provide surface protection. For instance, hybrid nanofluids can provide a protective coating on the surface of a flat plate due to the presence of nanoparticles. This coating can offer improved corrosion resistance, erosion resistance, and anti-fouling properties. Consequently, it can extend the lifespan of the flat plate and reduce maintenance requirements. In this study, we examined how several characteristics, such as variable viscosity, chemical reaction, thermal radiation and shape factor of nanoparticles, affect the flow of a hybrid nanofluid (H[Formula: see text]) through a flat plate. The equations required to represent the problem have been turned into a system of nonlinear ordinary differential equations, and this system has been unraveled by means of the bvp4c solver. Outcomes are provided for three instances related to shape factor i.e. Platelet, Cylinder and Spherical. Using Multiple Linear Regression (MLR), we investigated how physical parameters of concern together with friction factor, are affected by a variety of parameters. It is remarked that the fluid’s velocity lessens as the variable viscosity parameter enhances. It is discovered that the temperature profile increases with the rise in exponential heat source parameter ([Formula: see text]). It is discovered that when [Formula: see text], the Nusselt number declines by 0.03588 (Platelet shape), 0.03562 (Cylinder shape), and 0.03489 (Spherical shape). It has been noted that magnetic field parameter (Mg) reduces the coefficient of skin friction. At [Formula: see text], the skin friction coefficient is seen to drop at a rate of 1.15018 (Platelet shape), 1.14871 (Cylinder shape), and 1.14476 (Spherical shape). There is an enhancement in the Sherwood number with the rise in Schmidt number (St) and chemical reaction parameter (Cr). At [Formula: see text] the Sherwood number is seen to rise at a rate of 0.248303 (Platelet shape), 0.248344 (Cylinder shape), and 0.248447 (Spherical shape). Furthermore, it is detected that the fluid’s temperature rises as the thermal radiation parameter enhances and the entropy generation increases as the variable viscosity parameter increases.

The blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra

Abstract To every finite metric space X, including all connected unweighted graphs with the minimum edge-distance metric, we attach an invariant that we call its blowup-polynomial $p_X(\{ n_x : x \in X \})$ . This is obtained from the blowup $X[\mathbf {n}]$ – which contains $n_x$ copies of each point x – by computing the determinant of the distance matrix of $X[\mathbf {n}]$ and removing an exponential factor. We prove that as a function of the sizes $n_x$ , $p_X(\mathbf {n})$ is a polynomial, is multi-affine, and is real-stable. This naturally associates a hitherto unstudied delta-matroid to each metric space X; we produce another novel delta-matroid for each tree, which interestingly does not generalize to all graphs. We next specialize to the case of $X = G$ a connected unweighted graph – so $p_G$ is “partially symmetric” in $\{ n_v : v \in V(G) \}$ – and show three further results: (a) We show that the polynomial $p_G$ is indeed a graph invariant, in that $p_G$ and its symmetries recover the graph G and its isometries, respectively. (b) We show that the univariate specialization $u_G(x) := p_G(x,\dots ,x)$ is a transform of the characteristic polynomial of the distance matrix $D_G$ ; this connects the blowup-polynomial of G to the well-studied “distance spectrum” of G. (c) We obtain a novel characterization of complete multipartite graphs, as precisely those for which the “homogenization at $-1$ ” of $p_G(\mathbf { n})$ is real-stable (equivalently, Lorentzian, or strongly/completely log-concave), if and only if the normalization of $p_G(-\mathbf { n})$ is strongly Rayleigh.

Reconciling absence of vDVZ discontinuity with absence of ghosts in nonlocal linearized gravity

The modern massive gravity theories resolve a historical tension between the absence of the so called vDVZ mass discontinuity and the absence of ghosts via a fine tuned gravitational potential and a sophisticated screening mechanism. Those theories have originated the modern covariant bimetric models which are local, ghost free and cosmologically viable apparently, they contain a massive plus a massless graviton in the spectrum. It seems hard to solve the mentioned tension if we do insist in a model with a minimal number of degrees of freedom, with only one massive spin-2 particle in the spectrum, even if we allow nonlocal theories. Here we show that this problem can be circumvented in linearized nonlocal theories by the introduction of exponential terms with infinite derivatives. The model admits non linear completions via nonlocal quadratic terms in curvatures. We also investigate the role of the exponential factors in linearized models where the graviton remains massless and a mass scale is introduced via nonlocal terms, they are also ghost free and approach the Einstein–Hilbert theory as we go much above the introduced mass scale.