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In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose–Einstein particles for the hard sphere model for bounded anisotropic initial data. The main idea of our proof is as follows: we first establish an intermediate equation which is closely related to the original equation and is relatively easily proven to have global in time and unique solutions, then we use the multi-step iterations of the collision gain operator to obtain a desired uniform L ∞ -bound for solutions of the intermediate equation so that if an initial datum is sufficiently small relative to the inverse of the Planck constant (which belongs to the case of very high temperature), then the corresponding solution of the intermediate equation becomes the solution of the original equation.

Vertical bone augmentation is an important challenge in dental implantology. Existing vertical bone augmentation techniques, along with bone grafting materials, have achieved certain clinical progress but continue to have numerous limitations. In order to evaluate the possibility of using biomaterials to develop bone substitutes, medical devices and/or new bone grafting techniques for vertical bone augmentation, it is essential to establish clinically relevant animal models to investigate their biocompatibility, mechanical properties, applicability and safety. The present review discusses recent animal experiments related to vertical bone augmentation. In addition, surgical protocols for establishing relevant preclinical models with various animal species were reviewed. The present study aims to provide guidance for selecting experimental animal models of vertical bone augmentation.

It is expected in physics that the homogeneous quantum Boltzmann equation with Fermi-Dirac or Bose-Einstein statistics and with Maxwell-Boltzmann operator (neglecting effect of the statistics) for the weak coupled gases will converge to the homogeneous Fokker-Planck-Landau equation as the Planck constant $\hbar$ tends to zero. In this paper and the upcoming work \cite{HLP2}, we will provide a mathematical justification on this semi-classical limit. Key ingredients into the proofs are the new framework to catch the {\it weak projection gradient}, which is motivated by Villani \cite{V1} to identify the $H$-solution for Fokker-Planck-Landau equation, and the symmetric structure inside the cubic terms of the collision operators., 57 pages with an Appendix

We study the long time behavior of measure-valued isotropic solutions \begin{document}$F_t$\end{document} of the Boltzmann equation for Bose-Einstein particles for low temperature. The global in time existence of such solutions \begin{document}$F_t$\end{document} that converge at least semi-strongly to equilibrium (the Bose-Einstein distribution) has been proven in previous work and it has been known that the long time strong convergence to equilibrium is equivalent to the long time convergence to the Bose-Einstein condensation. Here we show that if such a solution \begin{document}$F_t$\end{document} as a family of Borel measures satisfies a uniform double-size condition (which is also necessary for the strong convergence), then \begin{document}$F_t$\end{document} converges strongly to equilibrium as \begin{document}$t$\end{document} tends to infinity. We also propose a new condition on the initial datum \begin{document}$F_0$\end{document} such that a corresponding solution \begin{document}$F_t$\end{document} converges strongly to equilibrium.

Intraparotid facial nerve schwannoma (IFNS) is rare and its definite preoperative diagnosis is challenging.To improve available knowledge regarding the diagnosis of IFNS and to suggest an appropriate treatment plan.We retrospectively analyzed medical records of IFNS patients at our hospital. Inclusion criteria were surgery (from January 2000, to December 2016) for a parotid mass, pathologically diagnosed as a schwannoma.The study included 42 eligible patients who had undergone tumor resection from 5977 parotid tumor patients. Mostly presented hard-textured (18/39) or medium-textured (15/39), with limited mobility (21/39) mass (three tumors were not palpable). Their facial nerve function outcomes were House-Brackmann Grade I (n = 14), Grade II (n = 7), Grade III (n = 11), Grade IV (n = 5), Grade V (n = 3), and Grade VI (n = 2). Significant differences were noted in results based on different surgical methods used (p = .000) and tumor involvement (p = .002).A hard-textured tumor with limited mobility mass in the parotid gland should prompt the diagnosis of a schwannoma. Tumors involving main trunk usually lead to unsatisfactory facial nerve outcomes. Facial nerve preservation should always be essential, and stripping surgery or intracapsular enucleation could be the preferred surgical methods of choice.

It is necessary to explore the best treatment to eradicate trimethylamine [TMA] in air, since it is toxic and hazardous to the living organism. Photocatalysis, a low-cost and environmentally friendly technology, has been studied in comparison with photo-electrochemical catalysis in the removal of TMA gas. In this study, it is most quickly and efficiently degraded using Co-MoS2 composite catalyst in an integrated system of (PEC) photo-electrochemical catalysis. The performance of the catalyst and system was evaluated by TMA removal ratio. As a result, the catalyst has good degradation performance for TMA in the PEC system, which indicates that it has high photocatalytic activity and high apparent quantum efficiency. In addition, the stability of the Co-MoS2 catalyst in the PEC is better than in PC due to the presence of the external bias generated by the assisted electrochemistry in the PEC system.

The paper is a continuation of our previous work on the spatially homogeneous Boltzmann equation for Bose–Einstein particles with quantum collision kernel that includes the hard sphere model. Solutions $$F_t$$ under consideration that conserve the mass, momentum, and energy and converge at least weakly to equilibrium $$F_{\mathrm{be}}$$ as $$t\rightarrow \infty $$ have been proven to exist at least for isotropic initial data that have positive entropy, and $$F_t$$ have to be Borel measures for the case of low temperature. The new progress is as follows: we prove that the long time convergence of $$F_t(\{0\})$$ to the Bose–Einstein condensation $$F_{\mathrm{be}}(\{0\})$$ holds for all isotropic initial data $$F_0$$ satisfying the low temperature condition. This immediately implies the long time strong convergence to equilibrium. We also obtain an algebraic rate of the strong convergence for arbitrary temperature. Our proofs are based on entropy control, positive lower bound of entropy, Villani’s inequality for entropy dissipation, a suitable time-dependent convex combination between the solution and a fixed positive function (in order to deal with logarithm terms), the convex-positivity of the cubic collision integral, and an iteration technique for obtaining a positive lower bound of condensation.

We study long time behavior of the Bose–Einstein condensation of measure-valued solutions $$F_t$$ of the space homogeneous and velocity isotropic Boltzmann equation for Bose–Einstein particles at low temperature. We prove that if $$F_0\ge 0$$ is a non-singular Borel measure on $${{\mathbb R}}_{\ge 0}$$ satisfying a very low temperature condition and that the ratio $$F_0([0,\varepsilon ])/\varepsilon ^{\alpha }$$ is sufficiently large for all $$\varepsilon \in (0, R]$$ for some constants $$0 0$$ , then there exists a solution $$F_t$$ of the equation on $$[0,+\infty )$$ with the initial datum $$F_0$$ such that $$F_t(\{0\})$$ converges to the expected Bose–Einstein condensation as $$t\rightarrow +\infty $$ . We also show that such initial data $$F_0$$ exist extensively.

Xing Wang,1,* Guilan Zhang,2,* Feng Qi,3 Yongfeng Cheng,1 Xuguang Lu,1 Lu Wang,1 Jing Zhao,1 Bin Zhao1 1Shanxi Medical University Stomatological Hospital, Taiyuan, 2Department of Stomatology, Nanfang Hospital, Southern Medical University, Guangzhou, China; 3Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO, USA *These authors contributed equally to this work Abstract: Insulin is widely considered as a classical hormone and drug in maintaining energy and glucose homeostasis. Recently, insulin has been increasingly recognized as an indispensable factor for osteogenesis and bone turnover, but its applications in bone regeneration have been restricted because of the short periods of activity and uncontrolled release. In this study, we incorporated insulin-loaded poly lactic-co-glycolic-acid (PLGA) nanospheres into nano-hydroxyapatite/collagen (nHAC) scaffolds and investigated the bioactivity of the composite scaffolds in vitro and in vivo. Bioactive insulin was successfully released from the nanospheres within the scaffold, and the release kinetics of insulin could be efficiently controlled by uniform-sized nanospheres. The physical characterizations of the composite scaffolds demonstrated that incorporation of nanospheres in nHAC scaffolds using this method did not significantly change the porosity, pore diameters, and compressive strengths of nHAC. In vitro, the insulin-loaded nHAC/PLGA composite scaffolds possessed favorable biological function for bone marrow mesenchymal stem cells adhesion and proliferation, as well as the differentiation into osteoblasts. In vivo, the optimized bone regenerative capability of this composite scaffold was confirmed in rabbit mandible critical size defects. These results demonstrated successful development of a functional insulin–PLGA–nHAC composite scaffold that enhances the bone regeneration capability of nHAC. Keywords: insulin, composite scaffold, drug delivery system, bone tissue engineering&nbsp

We study regularity and finite time condensation of distributional solutions of the space-homogeneous and velocity-isotropic Boltzmann equation for Bose–Einstein particles for the hard sphere model. Global in time existence of distributional solutions had been proven before. Here we prove that the equation is locally and can be globally (in time) well-posed for the class of distributional solutions having finite moment of the negative order $$-1/2$$ , and solutions in this class with regular initial data are mild solutions in their regularity time-intervals. By observing a necessary condition on the initial data for the absence of condensation at some finite time, we also propose a sufficient condition on the initial data for the occurrence of condensation at all large time, and then using a positivity of a partial collision integral we prove further that the critical time of condensation can be strictly positive.

The paper considers the problem of the Bose-Einstein condensation in finite time for isotropic distributional solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles with the hard sphere model. We prove that if the initial datum of a solution is a function which is singular enough near the origin (the zero-point of particle energy) but still Lebesgue integrable (so that there is no condensation at the initial time), then the condensation continuously starts to occur from the initial time to every later time. The proof is based on a convex positivity of the cubic collision integral and some properties of a certain Lebesgue derivatives of distributional solutions at the origin. As applications we also study a special type of solutions and present a relation between the conservation of mass and the condensation.

The paper considers backward solutions of the spatially homogeneous Boltzmann equation for Maxwellian molecules with angular cutoff. We prove that if the initial datum of a backward solution has finite moments up to order >2, then the backward solution must be an equilibrium, i.e. a Maxwellian distribution. This gives a partial positive answer to the Villani’s conjecture on a global irreversibility of Maxwellian molecules.

Background The objectives of the present study were to investigate the reliability and outcomes of computer-assisted techniques in mandibular reconstruction with a fibula flap and verify whether the surgical navigation system was feasible in mandible reconstructive surgery. Methods Eight cases were enrolled in the computer assisted surgery (CAS) group and 14 cases in the traditional group. The shaping and fixation of the fibula grafts were guided by computer assisted techniques, which could be monitored with the BrainLAB surgical navigation system. The variation of mandible configuration was evaluated by CT measurement in the Mimics software, including the variation of length, width, height and gonial angle of the mandible. The 3D facial soft tissue alteration was also analyzed in 3D chromatogram by Geomagic software. Results All 22 fibula flaps survived. The mandibular configurations and facial contours had a better clinic result in the CAS group. The length, width, height and gonial angle of the reconstructive mandible were more similar to the original one. The Wilcoxon rank sum test analysis suggested significant differences in the measurements. The chromatographic analysis also visually showed superiority over the traditional group. Conclusions The computer assisted surgical navigation method used in mandibular reconstruction is feasible and precise for clinical application. The contour of the reconstructed mandible and facial symmetry are improved with computer techniques.

The paper considers the convergence to equilibrium for measure solutions of the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. We prove the exponential sharp rate of strong convergence to equilibrium for conservative measure solutions having finite mass and energy. The proof is based on the regularizing property of the iterated collision operators, exponential moment production estimates, and some previous results on the exponential rate of strong convergence to equilibrium for square integrable initial data. We also obtain a lower bound of the convergence rate and deduce that no eternal solutions exist apart from the trivial stationary solutions given by the Maxwellian equilibrium. We finally use these convergence rates in order to deduce global-in-time strong stability of measure solutions., Comment: 60 pages -- some typos corrected and explanations added in the new version

The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L 1-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ *|γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫0 π b(cos θ)sin 3θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L ∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy.

Long time behavior of solutions of the spatially homogeneous Boltzmann equation for Bose–Einstein particles is studied for hard potentials with certain cutoffs and for the hard sphere model. It is proved that in the cutoff case solutions as time $$t\rightarrow\infty$$ converge to the Bose–Einstein distribution in L1 topology with the weighted measure $$(\varrho +|v|^2)dv$$ , where $$\varrho=1$$ for temperature $$T\geq T_c$$ and $$\varrho=0$$ for T

The paper considers the spatially homogeneous Boltzmann equation for Bose-Einstein particles (BBE). In order to include the hard sphere model, the equation is studied in a weak form and its solutions (including initial data) are set in the class of isotropic positive Borel measures and therefore called isotropic distributional solutions. Stability of distributional solutions is established in the weak topology, global existence of distributional solutions that conserve the mass and energy is proved by weak convergence of approximate L1-solutions, and moment production estimates for the distributional solutions are also obtained. As an application of the weak form of the BBE equation, it is shown that a Bose-Einstein distribution plus a Dirac dt-function is an equilibrium solution to the BBE equation in the weak form if and only if it satisfies a low temperature condition and an exact ratio of the Bose-Einstein condensation.

The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under a cutoff condition on the collision kernel, we prove a strong stability in L 1 topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L 1 to equilibrium under a high temperature condition. The basic tools used are moment-production estimates and the strong compactness of the collision gain term.

We consider the spatially homogeneous Boltzmann equation for Maxwellian molecules and general finite energy initial data: positive Borel measures with finite moments up to order 2. We show that the coefficients in the Wild sum converge strongly to the equilibrium, and quantitatively estimate the rate. We show that this depends on the initial data F essentially only through on the behavior near r=0 of the function J F (r)=∫|v|>1/r |v|2 dF(v). These estimates on the terms in the Wild sum yield a quantitative estimate, in the strongest physical norm, on the rate at which the solution converges to equilibrium, as well as a global stability estimate. We show that our upper bounds are qualitatively sharp by producing examples of solutions for which the convergence is as slow as permitted by our bounds. These are the first examples of solutions of the Boltzmann equation that converge to equilibrium more slowly than exponentially.

The objective of this study was to develop an electrophysiological method for intraoperative localization of the trigeminal nerve branches during radiofrequency thermocoagulation (RFTC).Twenty-three patients who were scheduled to undergo RFTC were included. The trigeminal nerve root was stimulated through the foramen ovale using the radiofrequency cannula. Antidromic responses were recorded from the target division through supraorbital, infraorbital, and mental foramina electrodes, and an additional electrode at the masseter muscle. Sensory and motor action responses, as well as verbal and masseter contraction responses, were recorded and correlated.The antidromic responses were easily recorded in the target division in all 23 patients, and they were invariably correlated with the patient's verbal responses. The potentials were recorded successively from V1 to V3. The amplitude in each division before and after RFTC showed little difference in response to electrical stimulation with the same current. The motor trigeminal nerve action potentials were recorded in 10 patients; 7 of these patients had postoperative masseter muscle weakness, while the remaining 3 had normal masseter muscle function. Potentials with low amplitudes were usually obtained from neighboring divisions, but no unexpected denervation of any branches was observed. All the patients experienced immediate pain relief after the procedure.This technique is sensitive and easy to apply. The sensory and motor potentials matched the verbal responses and the complications. Although it cannot completely substitute for the patient's verbal response, this approach is helpful in uncooperative patients, and it predicts and reduces the incidence of masseter muscle weakness. The use of these complementary techniques could increase the chances of treatment success.

The paper considers a modified spatially homogeneous Boltzmann equation for Fermi–Dirac particles (BFD). We prove that for the BFD equation there are only two classes of equilibria: the first ones are Fermi–Dirac distributions, the second ones are characteristic functions of the Euclidean balls, and they can be simply classified in terms of temperatures: T>2/5TF and T=2/5TF, where TF denotes the Fermi temperature. In general we show that the L∞-bound 0≤f≤ 1/e derived from the equation for solutions implies the temperature inequality T≥2/5TF, and if T>2/5TF, then f trend towards Fermi–Dirac distributions; if T=2/5TF, then f are the second equilibria. In order to study the long-time behavior, we also prove the conservation of energy and the entropy identity, and establish the moment production estimates for hard potentials.

Nonnegativity of solutions of the Boltzmann equation with nonnegative initial data is the most necessary physical property. This paper considers collision kernels with angular cut-off. We prove that for collision kernels of non-soft potentials, if fis a mild solution of the Boltzmann equation on R 3× R 3× [0, t ∞) and satisfies the following condition (which includes the case of x-priodic solutions) then fmust be nonnegative on R 3× R 3× [0, t ∞), where 0 < t ∞≤ ∞. In particular, for Maxwell molecules model, if fis an x-preodic solution and satisfies then fis nonnegative on R 3× R 3× [0, t ∞). Under similar conditions, the same results about nonnegativity of solutions hold also true for collision kernels of soft potentials. As an application, we show that these conditions are easily satisfied by the solutions fobtained before which are close to the global Maxwellian M(v) in the form f(x, v, t) = M(v) + [M(v)]1/2 F(x, v, t) (i.e., Fare small functions), and therefore fare actually nonnegative.

Under some strong cutoff conditions on collision kernels, global existence, local stability, entropy identity, conservation of energy, and moment production estimates are proven for isotropic solutions of a modified (quantum effect) Boltzmann equation for spatially homogeneous gases of Bose–Einstein particles (BBE). Then applying these results with the biting-weak convergence, some results on the long-time behavior of the conservative isotropic solutions of the BBE equation are obtained, including the velocity concentration at very low temperatures and the tendency toward equilibrium states at very high temperatures.

For nonsoft potential collision kernels with angular cutoff, we prove that under the initial condition f0(v)(1+|v|2+|logf0(v)|)∈L1(R3), the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous Boltzmann equation in the class L∞([0, ∞); L12(R3))∩C1([0, ∞); L1(R3)) [where L1s(R3)={f∣f(v)(1+|v|2)s/2∈L1(R3)}], and in this class, the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy. Moreover, for hard potentials and the hard-sphere model, a local stability result for conservative solutions (i.e., satisfying the conservation of mass, momentum, and energy) is obtained. As an application of the local stability, a sufficient and necessary condition on the initial data f0 such that the conservative solutions f belong to L1loc([0, ∞); L12+β(R3)) is also given.

We prove some converse properties of long time limiting behavior (along the particle paths) of a class of spatial decay solutions of the Boltzmann equation. It is shown that different initial data f0 determine different long time limit functions $f_{\infty}(x,v) = \lim_{t\rightarrow \infty}f(x+tv,v,t)$, and for any given function F(x,v) which belongs to a function set, there exists a solution f such that $f_{\infty}=F$. Existence of such spatial decay solutions are proven for the inverse power potentials with weak angular cut-off condition and for the initial data f0 satisfying $f_{0}(x,v)\leq C(1+|x|^2+|v|^2)^{-k}$, or $f_{0}(x,v) \leq C(1+|x-v|^2)^{-k}$ , etc. For the soft potentials, the solutions may have ``locally infinite particles," i.e., $\int_{{\bf R}^3}f(x,v,t)dv\equiv\infty.$

This paper presents an essentially simple and direct method to prove the regularizing properties of the collision gain term in the first equation of the Boltzmann hierarchy. Some corollaries of the main results of this paper are given to improve the previous results on the regularity of the gain term in the Boltzmann equation. An extension of a new fundamental result concerning separated variable kernels is also given to some general kernels.

We consider the problem of multivariate convex approximation by positive linear operators. LetEbe ak-dimensional compact convex set inRkwithk⩾2,Ω⊂Rkan open set containingE, and letL:C(E)→C1(Ω) be a positive linear operator. Our main result of this paper shows that ifLpreserves convexity and satisfiesLl=lonEfor alll∈P1(the space of affine functions), thenLis trivial (i.e.,Lf∈P1onEfor allf∈C(E)) andEis a simplex.

The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of \emph{weak measure solutions}, with and without angular cutoff on the collision kernel; the proof in particular makes use of an approximation argument based on the Mehler transform. Moment production estimates in the usual form and in the exponential form are obtained for these solutions. Finally for the Grad angular cutoff, we also establish uniqueness and strong stability estimate on these solutions., New version: many typos corrected, and more explanations added. 51 pages, to appear in J. Diff. Eq

In this paper, the disadvantage of using traditional histogram equalization for infrared image enhancement is discussed. Then by analyzing the human visual responds to the logarithm of image lightness, a modified method of histogram equalization algorithm is proposed based on the visual characteristic. The method can improve the displaying ability of image details through adjusting the pixel contrast which is out of vision. Using the method to enhance infrared image, which proves the effect of the modified method.

A tracking device of multiple target is proposed, whose field range reaches hemisphere airspace(sr) because of the using of IR Fish-eye system. The infrared ray is collected by Fish-eye lens, by this way can get the thermal image about the whole space, whose range depends on the lens used. Thanks to the Fish-eye system and Ptsi staring focal plane array, the tracking device can get a big range, that means can get multiple target at one time. Depends on the algorithm adopted to process the image has been gotten, the tracking device specify some points with intensive ray which means elevated temperature, and that will be the targets. At the next step after targets detection, the algorithm will compute out the speed and orientation of every target, then figure out a quotient-for-danger about every target. With this quotient, the algorithm can judge which one is the most dangerous from those flying to us, and it should be treated firstly, then the less dangerous ones, etc. To ensure the whole system run at real-time, all of the processing has to be finished at a moment. A TM320 DSP is adopted to run the algorithm. The result will be displayed at a LCD with every target labeled by their quotient-for-danger. The reaction speed and precision of this tracking device has been proved on our multiple target experiment platform.

Large field of view IR fish-eye system can survey real-time th e target in hemisphere airspace. For the single target, it can find the cooperative target and experimentalism easily. But multitasking for the multiple detecting, tracking and judging the level of threat it could find the cooperative target and prove the studied algorithms and hardware system very difficultly [1] . The paper brings forward an experiment system which is used for identifying multiple target. Through the system the simulation of the parameters in fairway i distance i direction and velocity are achieved. The system is composed of many controlled fountain of heat, which are made up of symmetrically heated flat and temperature controlled equipment. Each fountain of heat is fixed on the carrier moving free in three dimension space, in front of which diaphragms are fixed for changing the size of diaphragms and distributing of temperature. The fountain of heat moves on the different track at different speed and direction when it’s working. The experiment system is proved to be feasible and precise through simulating single target and tracking the plane and other targets. Based on this system, the algorithms of multi-target tracking are validated. Keywords o IR fish-eye system, Multiple target tracking , Experiment device, IR target simulation

The paper presents the algorithms of data process on multi-target tracking and threat level sequence in large visual area IR (infrared ray) fish-eye system. The targeting information is associated and filtered with the polar coordinates. Firstly,The characteristic point of every target is picked up and tracked with special restriction for each of them. Secondly,the parameters of fairway, which are gained by aberration revising and researching the characters of temperature area, are picked up from serial images. The threat level of attacking objects is sorted by the speed, acceleration and direction of all targets. Finding out the most prior target which is in the certain distance in order to make sure that effective warning information is emitted in time. The algorithms are proved to be quick and effective through simulation and the muiti-target experiment system developed by the writers.

Used infrared fisheye lens and PbSi staring focal plane array, we design a novel Infrared observing system. This observing system can observe and recognize the infrared dim and small target in hemispher airspace(2 µ sr.).

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le \gm, This version contains a strengthened theorem 3, on rate of convergence, considerably relaxing the hypotheses on the initial data, and introducing a new method for avoiding use of poitwise lower bounds in applications of entropy production to convergence problems

We propose here a linear blind multiuser detector, referred to as the Capon receiver, for space-time coded CDMA (code division multiple access) systems. The proposed Capon receiver is designed to pass desired signals without distortion, meanwhile minimizing the overall interference signals, irrespective of their origins. It is shown that the Capon receiver achieves similar performance in terms of the output SINR (signal-to-interference-and-noise ratio) to that of the optimum, linear, training-assisted MMSE (minimum mean squared error) receiver over a wide range of the input SNR (signal-to-noise ratio). It is also shown that the ratio of the output SINR of the Capon receiver to that of the MMSE receiver converges to a constant very close to one at high SNRs. The Capon receiver also yields a blind channel estimate which converges to the true channel parameters (within a scalar ambiguity) as the SNR increases. Simulation results are provided to support our study.