Regular Cone Research Articles

Moderate Signal Enhancement in Electrospray Ionization Mass Spectrometry by Focusing Electrospray Plume with a Dielectric Layer around the Mass Spectrometer's Orifice.

Electrospray ionization (ESI) is among the commonly used atmospheric pressure ionization techniques in mass spectrometry (MS). One of the drawbacks of ESI is the formation of divergent plumes composed of polydisperse microdroplets, which lead to low transmission efficiency. Here, we propose a new method to potentially improve the transmission efficiency of ESI, which does not require additional electrical components and complex interface modification. A dielectric plate-made of ceramic-was used in place of a regular metallic sampling cone. Due to the charge accumulation on the dielectric surface, the dielectric layer around the MS orifice distorts the electric field, focusing the charged electrospray cloud towards the MS inlet. The concept was first verified using charge measurement on the dielectric material surface and computational simulation; then, online experiments were carried out to demonstrate the potential of this method in MS applications. In the online experiment, signal enhancements were observed for dielectric plates with different geometries, distances of the electrospray needle axis from the MS inlet, and various compounds. For example, in the case of acetaminophen (15 μM), the signal enhancement was up to 1.82 times (plate B) using the default distance of the electrospray needle axis from the MS inlet (d = 1.5 mm) and 12.18 times (plate C) using a longer distance (d = 7 mm).

Fuzzy Fixed Point Theorems in Normal Cone Metric Space

In this paper, we proved a few fuzzy fixed point theorems in whole regular cone metric spaces, which can be the generalization of a few current consequences within side the literature.

Clinical observation of concentrated growth factor (CGF) combined with iliac cancellous bone and composite bone material graft on postoperative osteogenesis and inflammation in the repair of extensive mandibular defects

PurposeTo evaluate the effects of concentrated growth factor (CGF), combined with a mixture of iliac cancellous and composite bone materials, on the repair of extensive mandibular defects. Patients and MethodsThis clinical trial involved patients with mandibular defects caused by large cystic lesions. The test group comprised 16 patients who underwent CGF combined with iliac cancellous bone and composite bone materials to repair extensive mandibular defects, whereas the control group comprised eight patients who underwent vascularised free fibula grafts for mandibular segmental defects. Postoperative exudatum was collected from patients on the 1st, 2nd, 3rd, and 4th days postoperatively, and osteogenic factor, including alkaline phosphatase (ALP), osteocalcin (BGP), and procollagen type I N-terminal propeptide (PINP), and inflammatory cytokines were performed. Additionally, regular cone beam computed tomography (CBCT) scans were conducted before and after surgery. ResultsOn postoperative days 1–4, the expression levels of ALP, BGP, and PINP were higher in the test group, while those of IL-1α, IL-1β, IL-6, IL-8, and TNF-α, which were identified as co-differentially expressing inflammatory cytokines, were all down-regulated in the exudatum of the test group. Regular CBCT radiological scans revealed a significant osteogenic effect in the test group. ConclusionThe use of CGF combined with iliac cancellous bone and composite bone materials to repair extensive mandibular jaw defects facilitates bone formation and reductions in inflammation in the defect area in the short term, which deserves further research in clinical practice.

Representations of generalized Hardy functions in Beurling’s tempered distributions

Let B be a proper open subset in $${{\mathbb {R}}}^N$$ and C be a regular cone in $${{\mathbb {R}}}^N$$ . On our previous paper of Acta Scientiarum Mathematicarum 85, 595–611 (2019), we have defined the space of generalized Hardy functions, $$G_{\omega ^*,A}^p(T^B)$$ , $$1< p \le 2,$$ and $$A \ge 0$$ , and have shown that the functions in $$G_{\omega ^*,A}^p(T^B)$$ have distributional boundary values in the weak topology of Beurling tempered distributions, $${\mathcal {S}}_{(\omega )}^\prime $$ . In this paper we show that if the distributional boundary values are convolutors in Beurling ultradistributions of $$L_2$$ -growth, then the functions in $$G_{\omega ^*,0}^p(T^C)$$ , $$1< p \le 2,$$ can be represented as Cauchy and Poisson integral of the boundary values in $${\mathcal {S}}_{(\omega )}^\prime $$ .

Buckling of a double sector thin elastic plate: Analytical solution

Analytical solutions for elastic buckling and post-buckling geometries are scarce. The present work presents such a solution for a sample geometry, initially planar, which buckles into a complex 3D shape under tensile load. The assumptions are that the sample thickness is small, so that flexural stiffness is low compared to in-plane strain stiffness, and hence the sample can be considered inextensible. The initial geometry is composed of two disk angular sectors sharing a common edge. Under tensile loading, the two radial edges of each sector tend to align so that each half turns into two regular cone sectors. As the tensile load increases, the cone angle progressively decreases, but the same generic form holds the sample extension all along the tensile direction. Such a solution may be useful for validating numerical simulation tools, or stereo-vision shape measurement procedures.

Generalized Vector-Valued Hardy Functions

We consider analytic functions in tubes Rn+iB⊂Cn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone in Rn, an open convex cone in Rn, and a regular cone in Rn, with this latter cone being an open convex cone which does not contain any entire straight lines. The analytic functions satisfy several different growth conditions in Lp norm, and all of the resulting spaces of analytic functions generalize the vector valued Hardy space Hp in Cn. The analytic functions are represented as the Fourier–Laplace transform of certain vector valued Lp functions which are characterized in the analysis. We give a characterization of the spaces of analytic functions in which the spaces are in fact subsets of the Hardy functions Hp. We obtain boundary value results on the distinguished boundary Rn+i{0¯} and on the topological boundary Rn+i∂B of the tube for the analytic functions in the Lp and vector valued tempered distribution topologies. Suggestions for associated future research are given.

Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization Problems

In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well known that second-order optimality conditions involve the support function of the second-order tangent set. In this paper, we propose two approaches for establishing second-order optimality conditions for the nonconvex case. In the first approach, we extend the concept of the support function so that it is applicable to general nonconvex set-constrained problems, whereas in the second approach, we introduce the notion of the directional regular tangent cone and apply classical results of convex duality theory. Besides the second-order optimality conditions, the novelty of our approach lies in the systematic introduction and use, respectively, of directional versions of well-known concepts from variational analysis.

Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type

Let $f(\mathbf z,\bar{\mathbf z})$ be a convenient Newton non-degenerate mixed polynomial with strongly polar non-negative mixed weighted homogeneous face functions. We consider a convenient regular simplicial cone subdivision $\Sigma^*$ which is admissible for $f$ and take the toric modification $\hat{\pi} : X \to \mathbb{C}^n$ associated with $\Sigma^*$. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by $f(\mathbf z,\bar{\mathbf z})$ under the Assumption(*) (Theorem 32). This result is an extension of the first part of Theorem 11 ([4]) by M. Oka, which studies strongly polar positive cases, to strongly polar non-negative cases. We also consider some typical examples (§9).

Calixarene-Based lead receptors: an NMR, DFT and X-Ray synergetic approach

ABSTRACT The conformational changes of the homooxa adamantyl ketones 1 and 2, as well as of the calix[4]arene analogue derivative 3, all in the cone conformation, upon Pb2+ complexation were investigated by 1H, 13C, 207Pb NMR and proton spin-lattice relaxation times (T 1) experiments. The X-ray crystal structures of ketones 1 and 3 were determined. The inclusion of an acetonitrile molecule in the hydrophobic cavity of the ligands was observed in the solid state. In solution, inclusion was observed only in the case of Pb2+ ⊂ ketone 3 complex. DFT calculations were also performed to complement the NMR conformational analysis and to bring further insights to the cation complexation. The data confirmed the formation of 1:1 complexes between Pb2+ and the ligands, and that the cation is located inside the cavity defined by the phenoxy and carbonyl oxygen atoms. In general, the ligand conformations became closer to a regular cone upon complexation, with the binding models found for the three ketones through the NMR studies corroborated by the DFT calculations.

On the calm b-differentiability of projector onto circular cone and its applications

In this paper, we study a concept on the calm B-differentiability, a new kind of generalized differentiabilities for a given vector function introduced by Ye and Zhou in 2017, of the projector onto the circular cone. Then, we discuss its applications in mathematical programming problems with circular cone complementarity constraints. Here, this problem can be considered to be a generalization of mathematical programming problems with second-order cone complementarity constraints, and thus it includes a large class of mathematical models in optimization theory. Consequently, the obtained results for this problem are generalized, and then corresponding results for some special mathematical problems can be implied from them directly. For more detailed information, we will first prove the calmly B-differentiable property of the projector onto the circular cone. This result is not easy to be shown by simply resorting to those of the projection operator onto the second-order cone. By virtue of exploiting variational techniques, we next establish the exact formula for the regular (Fréchet) normal cone (this concept was proposed by Kruger and Mordukhovich in 1980) to the circular cone complementarity set. Note that this set can be considered to be a generalization of the second-order cone complementarity set. In finally, the exact formula for the regular (Fréchet) normal cone to the circular cone complementarity set would be useful for us to study first-order necessary optimality conditions for mathematical programming problems with circular cone complementarity constraints. Our obtained results in the paper are new, and they are generalized to some existing ones in the literature.

Lipschitz-like property relative to a set and the generalized Mordukhovich criterion

In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone of a restricted graph of the set-valued mapping. We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set by virtue of the projection of the coderivative onto a tangent cone. Furthermore, by introducing a projectional coderivative of set-valued mappings, we establish a verifiable generalized Mordukhovich criterion for the Lipschitz-like property relative to a closed and convex set. We will study the representation of the graphical modulus of a set-valued mapping relative to a closed and convex set by using the outer norm of the corresponding projectional coderivative value. For an extended real-valued function, we will apply the obtained results to investigate its Lipschitz continuity relative to a closed and convex set and the Lipschitz-like property of a level-set mapping relative to a half line.

Asymptotic behavior and stability of mean curvature flow with a conical end

If the initial hypersurface of an immortal mean curvature flow is asymptotic to a regular cone whose entropy is small, the flow will become asymptotically self-expanding. Moreover, the expander that gives rise to the limiting flow is asymptotically stable as an equilibrium solution of the normalized mean curvature flow.

Delivering total skin electron therapy using regular electron cones

This study presents a technique requiring relatively simple supporting devices and protection accessories for treating conditions like mycosis fungoides in which a uniform radiation dose to the whole body can be achieved by using the regular largest electron cone instead of HDRe[Formula: see text] mode in one treatment course. The regular cone total skin electron therapy technique presented in this study is able to deliver a uniform radiation dose to the patient’s skin surface. The result is satisfying when compared with the High Dose Rate e[Formula: see text] (HDRe[Formula: see text]) Stanford Six Field Technique.

The Cheng-Yau metrics on regular convex cones as harmonic immersions into the symmetric space of positive definite real symmetric matrices

A Riemannian metric $g$ on a domain $\Omega$ in $ \mathbb{R}^n$ defines a map $F_g$ from $(\Omega,g)$ into the symmetric space of positive definite real symmetric $n \times n$ matrices $(\textrm{Sym}^+(n),h)$, where $h$ is the Cheng-Yau metric on $\textrm{Sym}^+(n)$. We show that the map $F_g$ is a harmonic immersion if $\Omega$ is a regular convex cone and $g$ is the Cheng-Yau metric on $\Omega$. We also prove that the map $F_g$ is totally geodesic if $\Omega$ is a homogeneous self-dual regular convex cone and $g$ is the Cheng-Yau metric on $\Omega$.

Best proximity point of Zamfirescu contractions of Perov type on regular cone metric spaces

Best proximity point of Zamfirescu contractions of Perov type on regular cone metric spaces

New Sharp Necessary Optimality Conditions for Mathematical Programs with Equilibrium Constraints

In this paper, we study the mathematical program with equilibrium constraints formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. We derive a new necessary optimality condition which is sharper than the usual M-stationary condition and is applicable even when no constraint qualifications hold for the corresponding mathematical program with complementarity constraints reformulation.

Paley–Wiener-type theorem for analytic functions in tubular domains

Herein, a weighted version of the Paley–Wiener-type theorem for analytic functions in a tubular domain over a regular cone is obtained by using Hp space methods. Then, the classical n-dimensional Paley–Wiener theorem is generalized to a case wherein 0<p<2. Finally, a version of the edge-of-the-wedge theorem is obtained as an application of the weighted theorems.

Idiopathic epiretinal membrane surgery: safety, efficacy and patient related outcomes.

This review aims to give to the reader an overview selectively oriented on safety and efficacy of surgery, providing concise and direct answers about crucial questions of trainees and experts. Surgery for idiopathic epiretinal membrane (ERM) is a safe and effective procedure that can achieve long-term stable postoperative visual and anatomical improvement, with an overall low recurrence and complication rate. Young patients, with a short onset of symptoms and with better initial visual acuity achieve higher levels of visual outcome. The preoperative degree of metamorphopsia is the prognostic factor for their postoperative degree. Successful results may be obtained in eyes with specific optical coherence tomography criteria, such as thin ganglion cell layers, thin internal plexiform layer, longer photoreceptors outer segment, regular ellipsoid zone and cone outer segment tips line, and without ectopic inner foveal layer. Internal limiting membrane peeling demonstrates positive anatomical and functional outcomes, but final positions about its safety remain controversial.

Best Proximity Point Results for Quasi Contractions of Perov Type in Non-Normal Cone Metric Space

In this paper, we study the notion of Ciric-Perov quasi contraction and Fisher-Perov quasi contraction and prove some best proximity point theorems for such contractions in the frame work of non-normal regular cone metric spaces. We give an example to support our result. Our results extend and generalized many existing results in literature.

Best Proximity Point Theorems of C-class Functions in Regular Cone Metric Spaces

Best Proximity Point Theorems of C-class Functions in Regular Cone Metric Spaces