In this paper, we study the semilinear pseudo-parabolic equations $\displaystyle u_{t} - \triangle_{\mathbb{B}}u - \triangle_{\mathbb{B}}u_{t} = \left|u\right|^{p-1}u$ on a manifold with conical singularity, where $\triangle _{\mathbb{B}}$ is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary $x_{1} = 0$. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence and nonexistence of global weak solution: for the low initial energy $J(u_{0})<d$, the solution is global in time with $I(u_{0}) >0$ or $\displaystyle\Vert \nabla_{\mathbb{B}}u_{0}\Vert_{L_{2}^{\frac{n}{2}}(\mathbb{B})} = 0$ and blows up in finite time with $I(u_{0}) < 0$; for the critical initial energy $J(u_{0}) = d$, the solution is global in time with $I(u_{0}) \geq0$ and blows up in finite time with $I(u_{0}) < 0$. The decay estimate of the energy functional for the global solution and the estimates of the lifespan of local solution are also given.

Total Hip Arthroplasty (THA) is a common surgical procedure used to treat hip osteoar-thritis and other joint conditions that cause pain and functional limitation. Traditionally, THA has been most performed in elderly patients, but in recent years there has been an in-crease in hip arthroplasties in young patients. Femoral prosthesis rupture is a rare but sig-nificant complication that can also occur in young patients undergoing total hip arthro-plasty (THA). Some of the factors that can contribute to femoral prosthesis ruptures include abnormal overload, defects in the design lack of geometric fit, type of materials used in the stem and femoral head connection. The aim of this study is to analyze the criticalities in the contact between the femoral head and the stem neck. In particular, the two types of con-tacts will be taken into consideration: proximal and distal and through the finite element method (FEA) the criticalities will be defined. The results show that in the proximal contact the voltages are higher than 500 Mpa. This is due to the fact that there are higher circum-ferential voltages. In addition, to prevent bacterial infiltration or debris from the outside, the distal connection is the recommended one.

Conical emission is a typical nonlinear phenomenon that occurs when the femtosecond laser pulses interact with transparent media. In this work, the conical emission induced by two kinds of typical vortex beams (i.e., Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams) in water is experimentally studied. By recording the light spots of different wavelengths on the screen, the characteristics of the conical emission induced by femtosecond vortex beams are studied. It is found that the spots of the supercontinuum induced by the two kinds of vortex beams differ greatly from each other: The spots of the supercontinuum induced by the BG beam are a set of concentric rings like a rainbow with a white center, while the whit light spot in the case of the LG beam are a circular white disk, which is different from the commonly observed white light spots. By measuring the maximum divergence angle, it is observed that the divergence angle increases with the decrease of the wavelength, while the TC merely affects the divergence angle, which is explained from the formation mechanism of conical emission in terms of self-phase modulation. We hope this work can be helpful to the understanding of interaction between the intense laser pulses and matters.

In order to properly cover different scenarios, radiation patterns of antennas should be accordingly adjusted before fabrication. However, most antennas are unable to provide both broadside beam and designable conical beam which are usually-used radiation patterns for radio coverage. In this paper, a planar Circular Polarized (CP) annular Leaky-Wave Antenna (LWA) with conical beam is proposed, which is realized on annular Substrate-Integrated Waveguide (SIW). Broadside beam or conical beam could be easily obtained by fabricating the LWA with modified structural parameters. The central operating band is 5.8 GHz. The LWA allows only the -1th spatial harmonic to radiate, while the fundamental wave and other spatial harmonics are suppressed in slow wave mode. In order to validate the design effectiveness, two examples for broadside beam and conical beam radiation are fabricated and measured. The measurement results show good agreement with the simulation results. The proposed LWA presents a promising radiation performance and is a good candidate for wireless communication applications.

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of $G$-type.

Background: To compare the loss of preload in absence of loading and after a fixed number of ideal masticatory cycles in two different connection systems using all-on-four prosthetic model. Methods: Two equal models of an edentulous mandible rehabilitated with all-on-four technique with two types of abutment system (MUA and OT-Bridge) supporting a hybrid prosthesis, were used. Initial torque values of the prosthetic fixing screw, after ten minutes from initial screw tightening and after 400000 masticatory cycles were registered using a mechanical torque gauge. Differences between initial and final torque values were reported for each anchoring system and the two systems were finally compared. Results: No statistically significant differences regarding the loss of preload between MUA and OT-Bridge system were found after 400000 masticatory cycles; however, in MUA system it was found between anterior and posterior implant screws. A significant difference in preload loss was found only for MUA system comparing the initial screw torque to that measured after 10 minutes from the tightening in absence of cyclic loadings. Conclusions: MUA and OT-Bridge are reliable prosthetic anchoring systems able to tolerate repeated masticatory cycles also on distal cantilever in all-on-four rehabilitation model without any significant loss of preload in screw tightening

The development of novel coherent and brilliant sources, such as soft X-ray Free Electron Laser (FEL) and High Harmonic Generation (HHG) enables new ultrafast analysis of the electronic and structural dynamics of a wide variety of materials. Soft X-ray FEL delivers high brilliance beams with short pulse duration, high spatial coherence and photon energy tunability. In com-parison with FELs, HHG X-ray sources are characterized by a wide spectral bandwidth and few to sub-femtosecond pulses. The approach will lead to time-resolved reconstruction of molecular dynamics, shedding light on different photochemical pathways. The high peak brilliance of soft X-ray FELs facilitates investigations in nonlinear regime, while the broader spectral bandwidth of the HHG sources may provide the simultaneous probing of multiple components. Significant technical breakthroughs in these novel sources are under way to improve brilliance, pulse dura-tion, and to control spectral bandwidth, spot size, and energy resolution. Therefore, in the next few years, the new generation of soft X-ray sources combined with novel experimental tech-niques, new detectors, and computing capabilities will allow the study of several extremely-fast dynamics, such as vibronic dynamics. In the present review, we shortly discuss recent devel-opments in experiments, performed with soft X-ray FELs and HHG sources, operating near car-bon K-absorption edge, being a key atomic component in biosystems and soft materials. Differ-ent spectroscopy methods such as time-resolved pump-probe techniques, nonlinear spectrosco-pies and photoelectron spectroscopy studies have been addressed in an attempt of a better un-derstanding of fundamental physico-chemical processes

Keywords: artificial bone; conical implants; cylindrical implants; dental implants; implant stability quotient; insertion torque; polyurethane; post-extraction sites; removal torque.

Photophysical properties of a series of bis(arylydene)cycloalkanone dyes with various donor substituentns are studied by quantum chemistry. Their capacity for luminescence and nonradiative relaxation through trans-cis isomerization is related to their structure, in particular, to the donor capacity of the substituents and the degree of conjugation due to the central cycloalkanone moiety. It is shown that cyclohexanone central moiety introduces distortions and disrupts the conjugation, thus leading to a nonmonotonic change in their properties. The increasing donor capacity of the substituents causes increase in the HOMO energy (raise of the oxidation potential) and decrease in the HOMO-LUMO gap, which results in the red shift of the absorption spectra. The ability of the excited dye to relax through fluorescence or through trans-cis isomerization is governed by the height of the barrier between the Franck–Condon and S1-S0 conical intersection regions on the potential energy surface of the lowest π-π* excited state. This barrier also correlates with the donor capacity of the substituents and the degree of conjugation between the central and donor moieties. The calculated fluorescence and trans-cis isomerization rates are in good agreement with the observed fluorescence quantum yields.

By generalizing the notion of pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

The paper describes a new formula for calculating the mutual inductance between a thin conical sheet inductor and a filamentary circular loop, which are coaxial. The presented formula is derived semi-analytically using the complete elliptic integrals of the first, second, and the third kind, along with the integral term which will be solved numerically. The results are validated using double and single integration methods, as well as the semi-analytical formula. The mutual inductance between a thin wall solenoid and a filamentary circular loop can be obtained using the new formula for the conical coil and circular loop. Presented formulas can be useful in various applications, such as broadband RF and wireless power transfer systems that utilize conical inductors. Overall, the paper presents a valuable contribution to the field of inductor design and can be useful in various applications involving conical inductors.