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Using the folding procedure, we investigate the bound state of the $\Omega$+$\alpha$ system based on $\Omega$-$N$ ($^{5}S_{2}$) HAL QCD potential. Previous theoretical analyses have indicated the existence of a deeply bound ground state, which is attributed to the strong $\Omega$-nucleon interaction. By employing well-established parameterizations of nucleon density within the alpha particle, and the central HAL QCD $\Omega$-$N$ potential, we performed numerical calculations for the folding $\Omega$-$\alpha$ potential. Our results show that the $V_{\Omega\alpha}(r)$ potential can be accurately fitted using a Woods-Saxon function, with a phenomenological parameter $R = 1.1A^{1/3} \approx 1.74$ fm ($A=4$) in the asymptotic region where $2 < r < 3$ fm. We provide a thorough description of the corresponding numerical procedure. Our evaluation of the binding energy of the $\Omega$+$\alpha$ system within the cluster model is consistent with both previous and recent reported findings. To further validate the folding procedure, we also calculated the $\Xi$-$\alpha$ folding potential based on a simulation of the ESC08c $Y$-$N$ Nijmegen model. A comprehensive comparison between the $\Xi$-$\alpha$ folding and $\Xi$-$ \alpha$ phenomenological potentials is presented and discussed., Comment: 9 pages, 3 Figures

We investigate the $^{9}_{\phi}$Be and $^{6}_{\phi\phi}$He hypernuclei within the framework of the three-body cluster model %specifically as the $\phi$+$\alpha$+$\alpha$ and $\phi$+$\phi$+$\alpha$ systems, using the Faddeev formalism in configuration space. The $\phi$-$\alpha$ potential is determined through a folding procedure of the HAL QCD $\phi$-$N$ interaction in the $^4S_{3/2}$ channel with the matter distribution of $^4$He. The phenomenological $\alpha$-$\alpha$ and $\phi$-$\phi$ potentials are taken from the literature. Additionally, we construct a Wood-Saxon (WS) type interaction to simulate the $\phi$-$\alpha$ potential, also taken from the literature, based on an effective Lagrangian approach that includes $K\bar{K}$ meson loops in the $\phi$-meson self-energy. A comparison of binding energies obtained for both types of the $\phi$-$\alpha$ interactions reveals qualitative agreement. %between the obtained approaches. We predict the binding energy for the $^{9}_{\phi}$Be and $^{6}_{\phi\phi}$He hypernuclei as the mirror $\phi$+$\alpha$+$\alpha$ and $\phi$+$\phi$+$\alpha$ systems in the range of 1-11 MeV and 3-10 MeV, respectively. The range of values of the binding energies relies on the choice of the WS $\phi$-$\alpha$ interaction parameters., Comment: 11 pages, 3 figures

Within the framework of the Faddeev formalism in configuration space, we investigate bound states in the $\phi NN$ system with total isospin $T=0$ and $T=1$. The recently proposed lattice HAL QCD $\phi N$ potential in the $^{4}S_{3/2}$ channel does not support either $\phi N$ or $\phi NN$ bound states. The HAL QCD $\phi N$ potential in the $^{2}S_{1/2}$ channel suggests the bound states for $\phi N$ and $\phi NN (S=0)$ systems. However, the binding energies are highly sensitive to variations of the enhancement factor $\beta$, and the $\phi NN$ system is extremely strongly bound in the state $S=0$. Considering a spin-averaged potential %$(\frac{1}{3}V_{\phi N}^{1/2}+\frac{2}{3}V_{\phi N}^{3/2})$ for the state $S=1$ yields a bound state for $^3_\phi$H $(S=1)$ hypernucleus with the binding energy (BE) 14.9 MeV when $\beta = 6.9$. The evaluation of the BE for the $S=1$, $T=1$ three-body state results in 5.47 MeV. %Also, We evaluated the BE for the $S=1$, $T=1$ three-body state as 5.47 MeV. Additionally, calculations using our approach confirm the bound states for the $\phi NN$ ($S=2,T=0$ and $S=1, T=1$) system previously predicted with the Yukawa-type potential motivated by the QCD van der Waals attractive force, mediated by multi-gluon exchanges., Comment: 6 Pages, 1 figure

In the framework of the Faddeev equations in configuration space, we investigate the $K$(1460) meson as a resonant state of the $KK\bar{K}$ kaonic system. We perform calculations for the particle configurations $K^{0}K^{+}K^{-}$ and $K^{0}K^{+}\overline{{K}^{0}}$ within two models: the $ABC $ model, in which all three particles are distinguishable, and the $AAC$ model when two particles are identical. The models differ in their treatment of the kaon mass difference and the attractive Coulomb force between the $K^{+}K^{-}$ pair. We found that the Coulomb shift adds over 1 MeV to the three-body binding energy. The expected correction to the binding energy due to mass redistribution from $AA$ to $AB$ is found to be negligible, up to a maximum of 6\% of the relative mass correction. At the same time, the symmetry of the wave function is distorted depending on the mass ratio value. We found that the repulsive $KK$ interaction plays essential role in the binding energy of the $KK\bar K$ system and report the mass of 1461.8 or 1464.1 MeV for the neutral $K^{0}$(1460) and 1466.5 or 1468.8 MeV for the charged $K^{+}$(1460) resonances, respectively, depending on the parameter sets for $KK$ and $K\bar{K}$ interactions., Comment: 13 page, 4 figures

Based on the effective-mass concept, we perform the Faddeev calculations for a low-lying spectrum of 3$\alpha$ states in $^{12}$C nucleus. A three-body potential is used to describe the known breaking of the 3$\alpha$-cluster structure in the nucleus. We show that the contribution of the three-body potential to the Hamiltonian can be compensated by increasing/decreasing the $\alpha$-particle free mass. The effective-mass values are adjusted so that to reproduce the experimental data for the $^{12}$C nucleus. The energy dependence of the effective mass and the correlation to a three-body potential are discussed. We show that the coupling between the $0^+$ ($2^+$) levels forms a specific picture of anti-crossing on the energy/effective-mass plane., Comment: 13 pages, 6 figures

The cardinality of real numbers depends on the chosen axiomatic system and specific models of set theory. Under the ZF framework, real numbers are nondenumerable, but their exact cardinality remains debated due to possible extensions of the ZF axioms. We explored this issue by analyzing sets within the ZFC model and Wang's $\Sigma$ model. Set $S'$, within the ZFC framework, includes all pairs of algebraic numbers with a transcendental number inserted between each pair by a function $f$, which inserts an arbitrarily chosen transcendental number into every interval bounded by algebraic endpoints. This approach enables the representation of any number using these intervals. By employing the AC, one can identify intervals from any Cauchy sequence within $S'$. As each interval contains at least one number due to the function $f$, the intersections of these intervals contain numbers defined by these sequences, making a complete and countable set $S'$. The second set, created by inserting specifically defined transcendental numbers between algebraic numbers, starts with the sequence of algebraic numbers as the 0-th layer in Wang's $\Sigma$ model. A diagonal procedure applied to that layer generates a set of transcendental numbers which, combined with the 0-th layer, forms the $\Sigma_1$ layer. Continuing this recursive process results in a set equivalent to $S'$. This suggests that all constructive real numbers are countable, challenging the traditional diagonal argument. The AC is crucial for selecting transcendental numbers and identifying intervals and sequences, making the set $S'$. This might resonate with constructivists who oppose the AC. However, further analysis revealed conflicts between proofs of non-denumerability and the Nested Interval Property, indicating a need to reevaluate the countability of real numbers., Comment: Presented as an invited talk at the International Conference Constructive Mathematics Foundations and Practice (CM:FP) 2023: https://cmfp2023.masfak.ni.ac.rs/About_Conference.html, 28 pages

Three-body $AAB$ model for the $NN{\bar K}(s_{NN}=0)$ kaonic cluster is considered based on the configuration space Faddeev equations. Within a single-channel approach, the difference between masses of nucleons and kaons and the charge independence breaking of nucleon-nucleon interaction are taken into consideration. We definite the particle configurations in the system according to the particle masses and pair potentials. There are two sets of the particle configurations, $ ppK^-$, $np \bar{K^0}$ and $nn {\bar K}^0$, $npK^-$, charged and neutral. The three-body calculations are performed by applying $NN$ and $N\bar K$ phenomenological isospin-dependent potentials. The mass and energy spectra related to the particle configurations are presented. We evaluate the mass and energy uncertainties for the $NN\bar K$ model. An analogy to $NNN$ model for the $^3$H and $^3$He nuclei is proposed., Comment: 11 pages, 3 figures

A negative kink in excess conductivity is observed in p-type non-degenerate (moderate dopant concentration) silicon wafers when excited by a very narrow pulse of 532 nm laser appearing just after the complete positive decay of dark conductivity voltage. Most of the Si samples are pristine, and 3 of them are irradiated with gamma, proton, and chlorine ion beams respectively. These transients were examined using a time-resolved millimeter-wave conductivity apparatus (TRmmWC ) and the radiofrequency (RF) voltage response (after laser cut-off) consistently reveals a positive peak with nominal decay to zero followed by a negative kink. This negative photoconductivity (NPC) kink develops just after the complete decay of the positive photoconductivity (PPC) and lasts typically ~ 36 us. We present some data on general characteristics obtained from a set of normal (pristine doped Si) wafers and the gamma- and ion beam irradiated silicon (comparing with the parent pristine sample responses) for establishing possible new links that might enable estimation of defect parameters introduced in silicon.

We propose to study of the light speed isotropy and Lorentz invariance at Jefferson Laboratory by means of the measurements of the Compton Edge using of the Hall A/C existing experimental setup. Methodologically the same experiment has already been successfully elaborated at GRAAL experiment at the European Synchrotron Radiation Facility in Grenoble with 6 GeV electron beam. This Proposal states two goals expected to be reached at Jefferson Laboratory, both on Lorentz invariance: (a) the one-way light speed isotropy testing accuracy, following from conservative evaluations at numerical simulations, to about an order of magnitude better than was GRAAL's; (b) the dependence of the light speed on the velocity of the apparatus (Kennedy-Thorndike measurement) will be traced to an accuracy about 3 orders of magnitudes better than the available limits., Comment: Submitted to PAC45, Jefferson Laboratory, 38 pages, 14 figures

The hypernuclear systems $NN\Xi $ and $\Xi\Xi N$ are considered as an analogue of $nnp$ ($^3$H) nuclear system (with the notation as $AAB$ system). We use the recently proposed modification for the $s$-wave Malfliet-Tjon potential. The modification simulates the Extended-Soft-Core model (ESC08c) for baryon-baryon interactions. The $\Xi N$ spin/isospin triplet $(S, I)=(1, 1)$ potential generates a bound state with the energy $B_2(AB)$=1.56~MeV. Three-body binding energy $B_3$ for the states with maximal total isospin is calculated employing the configuration-space Faddeev equations. Comparison with the results obtained within the integral representation for the equations is presented. The different types of the relation between $B_2$ and $B_3(V_{AA}=0)$ are discussed., Comment: 11 pages, 4 figures

One of two postulates that are base for special relativity is that the laws of physics are invariant in all inertial systems, which has as a consequence that it is impossible for an observer to detect his motion through space. It will be shown that this is in a contradiction with the results of the Hafele-Keating experiment, which established that time is going faster in an airplane going westward than in that going eastward, if compared with clocks located on Earth. The result of the experiment allows not only to conclude that Earth is rotating toward east, but also to calculate the speed of Earth motion. Performing similar experiments it is also possible to measure Earth speed around the Sun, its speed in our galaxy, and actually its absolute speed. To generalize this for any inertial frame and to explain why an absolute speed can be assigned to any inertial frame we introduced the triplets paradox., Comment: 5 pages

The conventional $\Lambda$CDM cosmological model supplemented by the inflation concept describes the Universe very well. However, there are still a few concerns: new Planck data impose constraints on the shape of the inflaton potential, which exclude a lot of inflationary models; dark matter is not detected directly, and dark energy is not understood theoretically on a satisfactory level. In this brief sketch we investigate an alternative cosmological model with spherical spatial geometry and an additional perfect fluid with the constant parameter $\omega=-1/3$ in the linear equation of state. It is demonstrated explicitly that in the framework of such a model it is possible to satisfy the supernovae data at the same level of accuracy as within the $\Lambda$CDM model and at the same time suppose that the observed cosmic microwave background (CMB) radiation originates from a very limited space region. This is ensured by introducing an additional condition of light propagation between the antipodal points during the age of the Universe. Consequently, the CMB uniformity can be explained without the inflation scenario. The corresponding drawbacks of the model with respect to its comparison with the CMB data are also discussed., Comment: 23 pages, 4 figures

We present three-body nonrelativistic calculations within the framework of a potential model for the kaonic cluster ${K^-}pp$ using two completely different methods: the method of hyperspherical harmonics in the momentum representation and the method of Faddeev equations in configuration space. To perform a numerical benchmark, different $NN$ and antikaon-nucleon interactions are applied. The results of the calculations for the ground state energy for the ${K^-}pp$ system obtained by both methods are in reasonable agreement. Although the ground state energy is not sensitive to the $NN$ interaction, it shows very strong dependence on the $\overset{\_}{K}N$ potential. We show that the dominant clustering of the ${K^-}pp$ system in the configuration $\Lambda (1405)+p$ allows us to calculate the binding energy to good accuracy within a simple cluster approach for the differential Faddeev equations. The theoretical discrepancies in the binding energy and width for the ${K^-}pp$ system related to the different $NN$ and $\overset{\_}{K}N$ interactions are addressed., Comment: 14 pages, 3 figures

A high-energy photon polarimeter for astrophysics studies in the energy range from 10 MeV to 800 MeV is considered. The proposed concept uses a stack of silicon micro-strip detectors where they play the roles of both a converter and a tracker. The purpose of this paper is to outline the parameters of such a polarimeter and to estimate the productivity of measurements. Our study supported by a Monte Carlo simulation shows that with a one-year observation period the polarimeter will provide 6% accuracy of the polarization degree for photon energies above 100 MeV, which would be a significant advance relative to the currently explored energy range of a few MeV. The proposed polarimeter design could easily be adjusted to the specific photon energy range to maximize efficiency if needed., Comment: 19 pages, 7 figures

We point out a weak side of the commonly used determination of scalar cosmological perturbations lying in the fact that their average values can be nonzero for some matter distributions. It is shown that introduction of the finite-range gravitational potential instead of the infinite-range one resolves this problem. The concrete illustrative density profile is investigated in detail in this connection., Comment: 5 pages, 2 figures

Considered is spherical shell as a model for visible universe and parameters that such model must have to comply with the observable data. The topology of the model requires that motion of all galaxies and light must be confined inside a spherical shell. Consequently the observable universe cannot be defined as a sphere centered on the observer, rather it is an arc length within the volume of the spherical shell. The radius of the shell is 4.46 $\pm$ 0.06 Gpc, which is for factor $\pi$ smaller than radius of a corresponding 3-sphere. However the event horizon, defined as the arc length inside the shell, has the size of 14.0 $\pm$ 0.2 Gpc, which is in agreement with the observable data. The model predicts, without inflation theory, the isotropy and uniformity of the CMB. It predicts the correct value for the Hubble constant $H_0$ = 67.26 $\pm$ 0.90 km/s/Mpc, the cosmic expansion rate $H(z)$, and the speed of the event horizon in agreement with observations. The theoretical suport for shell model comes from general relativity, curvature of space by mass, and from holographic principle. The model explains the reason for the established discrepancy between the non-covariant version of the holographic principle and the calculated dimensionless entropy $(S/k)$ for the visible universe, which exceeds the entropy of a black hole. The model is in accordance with the distribution of radio sources in space, type Ia data, and data from the Hubble Ultra Deep Field optical and near-infrared survey., Comment: 7 pages 2 figures, Conference: Low Dimensional Physics and Gauge Principles, Yerevan, Armenaia, September 21-26, 2011

The main argument that Universe is currently expanding is observed redshift increase by distance. However, this conclusion may not be correct, because cosmological redshift depends only on the scaling factors, the change in the size of the universe during the time of light propagation and is not related to the speed of observer or speed of the object emitting the light. An observer in expanding universe will measure the same redshift as observer in contracting universe with the same scaling. This was not taken into account in analysing the SN Ia data related to the universe acceleration. Possibility that universe may contract, but that the observed light is cosmologically redshifted allows for completely different set of cosmological parameters $\Omega_M, \Omega_{\Lambda}$, including the solution $\Omega_M=1, \Omega_{\Lambda}=0$. The contracting and in the same time accelerating universe explains observed deceleration and acceleration in SN Ia data, but also gives significantly larger value for the age of the universe, $t_0 = 24$ Gyr. This allows to reconsider classical cosmological models with $\Lambda =0$. The contracting stage also may explain the observed association of high redshifted quasars to low redshifted galaxies., Comment: 4 pages, 1 figure, accelerating universe, cosmological redshift, dark energy, lambda

The cosmological redshifts z in the frequencies of spectral lines from distant galaxies as compared with their values observed in terrestrial laboratories, which are due to the scale factor a(t), frequently are interpret as a special-relativistic Doppler shift alone. We will demonstrate that this interpretation is not correct and that the contribution of the gravitational redshift is always present and significant. We will show that the gravitational redshift is actually about the same magnitude as the cosmological redshift, but that only for cosmological models without the dark energy component cosmological and gravitational redshift can be considered to be the same. Significant contribution of the gravitational redshift due to the gravitational field of the Universe, which is ignored in interpretation of the observational data, could have significant impact on cosmological theories. We will first calculate contributions of gravitational redshift to CMB and time dilation of Type Ia supernovae, and use it to explain the excess redshifts of quasars and active galaxies, and redshifts of companion galaxies of stars. We will show its possible implications on the interpretation of mass density of matter and mass as function of cosmological time. Finally we will demonstrate that taking into account gravitational redshift allows to interpret luminosity distance and surface brightness of distant galaxies to be consistent with the static universe cosmological models., Comment: Cosmology, cosmological and gravitational redshift, static universe, QSO, companion galaxies, mass-time dependance, 5 pages, 1 figure

Statistical properties of the single electron levels confined in the semiconductor (InAs/GaAs, Si/SiO2) double quantum dots (DQDs) are considered. We demonstrate that in the electronically coupled chaotic quantum dots the chaos with its level repulsion disappears and the nearest neighbor level statistics becomes Poissonian. This result is discussed in the light of the recently predicted "huge conductance peak" by R.S. Whitney at al. (Phys. Rev. Lett. {\bf 102}, 186802 (2009)) in the mirror symmetric DQDs., Comment: 4 pages, 9 figures

Assuming that the universe is homogenous and isotropic and applying Gauss' flux theorem for gravity, it follows that the gravitational field of the visible universe can be calculated as if the entire mass of the visible universe is located in one point. Taking into account that the mass of the visible universe is M=2x10^{53} kg, it appears that the entire visible universe is inside a {\it photon sphere} of radius R_{ps} = 14.3 Gpc. The current model for the visible universe must be corrected to account for the fact that measured horizon distance of 14.0 \pm 0.2 Gpc is not a straight line. Rather it is an arc of a circle with that length, because all photons are inside the photon sphere. Our model interprets the visible universe as a surface of a sphere (or an inside of a sphere shell) with radius 4.46 \pm 0.06 Gpc and an event horizon, located on that sphere (shell), with size of 14.0 \pm 0.2 Gpc. The model predicts CMB redshift and time dilatation of Type Ia supernovae by gravitation. It explains, without inflation theory, the isotropy and uniformity of the CMB. It predicts the correct value for the Hubble constant H_0 = 67.26 \pm 0.90 km/s/Mpc, the cosmic expansion rate H(z) in agreement with observations, and the speed of the event horizon. Through relativistic energy correction, our model also provides an explanation for critical density without use of dark matter. It explains that Type Ia supernovae redshifts are not related to the accelerated expansion of the universe and dark energy. It explains the reason for the established discrepancy between the non-covariant version of the holographic principle and the calculated dimensionless entropy (S/k) for the visible universe, which exceeds the entropy of a black hole. The model is in agreement with the distribution of radio sources in space, Type Ia data, and data from the HUDF optical and near-infrared survey., Comment: 8 pages, 5 figures, added figures and modified text. Subjects: General Physics (physics.gen-ph); Cosmology and Extragalactic Astrophysics (astro-ph.CO); Key words: cosmological model, photon sphere, shell model, CMB, CMB redshift, time dilatation, gravitation, universe expansion, holographic principle; dark matter and energy

Considered will be properties of the set of real numbers $\Re$ generated by an operator that has form of an exponential function of Gelfond-Schneider type with rational arguments. It will be shown that such created set has cardinal number equal to ${\aleph_0}^{\aleph_0}=c$. It will be also shown that the same set is countable. The implication of this contradiction to the countability of the set of real numbers will be discussed., Comment: 7 pages

Remarks on the Cantor's nondenumerability proof of 1891 that the real numbers are noncountable will be given. By the Cantor's diagonal procedure, it is not possible to build numbers that are different from all numbers in a general assumed denumerable sequence of all real numbers. The numbers created on the diagonal of the assumed sequence are not different from the numbers in the assumed denumerable sequence or they do not belong to that sequence., Comment: 5 pages

The proofs that the real numbers are denumerable will be shown, i.e., that there exists one-to-one correspondence between the natural numbers $N$ and the real numbers $\Re$. The general element of the sequence that contains all real numbers will be explicitly specified, and the first few elements of the sequence will be written. Remarks on the Cantor's nondenumerability proofs of 1873 and 1891 that the real numbers are noncountable will be given., Comment: 14 pages