Pp. 43–68. concentration and compactness arguments in

Christopher Scott Vance, Chelsea R. Carter, Raegan J. Carter, Maximo M. Del Valle, Jorge R. The effects of storage time and temperature on blood alcohol concentration were evaluated in this two-part study involving 34 ethanol-negative and 21 ethanol-positive volunteers. There was no increase in the concentration of ethanol-positive samples beyond the expected variability of the method, regardless of storage time or temperature. Many ethanol-positive samples demonstrated decreases in concentration during storage compared with the original immediate analysis.

The findings from this study support previous research, which demonstrates that microbial formation of ethanol in properly collected antemortem blood is unlikely. In forensic laboratories throughout the world, one of the most frequently performed analyses is the determination of a blood alcohol concentration BAC 1.

pp. 43–68. concentration and compactness arguments in

Samples obtained are primarily from individuals whom have been arrested for the suspicion of driving under the influence of alcohol DUI offenses.

Blood alcohol results are frequently litigated in San Diego County courts and arguments often ensue involving all aspects of the collection, storage and analysis of the blood sample. Recently, an increased number of arguments in local courts have centered on the acceptable length of time between blood collection and analysis of the blood for its ethanol concentration.

This has resulted in a number of questions involving the proper storage conditions for a blood sample. Unreliability of the result is often argued to be due to a theorized increase in ethanol concentration from the formation of ethanol by microorganisms usually Candida albicans in the blood sample, a process also known as fermentation.

This study was designed to test this contention as it applies to the analysis of antemortem whole blood for ethanol at the San Diego County Sheriff's Department Regional Crime Laboratory. The study sought to determine if indeed the formation of ethanol, presumably from fermentation, occurs in blood samples stored at room temperature or in those that have been exposed to the environment over time. In addition, data were collected to determine whether there was a significant difference in ethanol concentration between subject samples that were analyzed immediately after collection and those samples analyzed at a later time under various storage conditions.

These data were compared with previously published studies on the stability of ethanol in whole blood. The ethical standards of the Declaration of Helsinki 14 were used in planning and carrying out all aspects of the study. All subjects were volunteers who were informed in writing of the purpose and scope of the study prior to participating. In the ethanol-negative portion of the experiment, 34 subjects volunteered to participate after being informed that multiple tubes of blood would be drawn from a peripheral vein.

The subjects consisted of 10 males and 24 females with ages ranging from 26 to 65 years. Subjects were instructed to eat a normal breakfast the day of the study and, upon arrival at the laboratory, general demographics were recorded including the subjects' age, sex and food consumption that morning. Subjects were also asked if they had a personal history of diabetes or high blood sugar.

None of the study participants were aware of any current blood sugar or diabetes-related health concerns. Once a subject was confirmed to have a 0. Blood sample collection was performed in accordance with Title 17 of the California Code of Regulations 15 for the collection and analysis of ethanol in whole blood for traffic law enforcement.

The ethanol-free swabs used to clean the injection site prior to collection were commercially available Dynarex BZK Antiseptic Towelettes.

The time of the blood draw was noted and one blood tube from each subject was immediately taken to the laboratory for analysis, while the other two tubes from each subject were placed in room temperature storage for the remainder of the study. The sample that was analyzed immediately served as the baseline for comparison to all subsequent results and was then subjected to repeated exposure to the environment over the next 30 days. This method was chosen in an effort to increase exposure of the blood to the environment, possibly allowing microorganisms to enter the blood during sampling.AlvinoP.

Lions and G. TrombettiA remark on comparison results for solutions of second order elliptic equations via symmetrization. Amick and J.

TolandNonlinear elliptic eigenvalue problems on an infinite strip: global theory of bifurcation and asymptotic bifurcation. To appear in Math.

MR Zbl AuchmutyExistence of axisymmetric equilibrium figures.

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Auchmuty and R. RealsVariational solutions of some nonlinear free boundary problems. BerestyckiT. Gallouet and O. Kavianwork in preparation. Berestycki and P. LionsNonlinear scalar field equations. Paris, t. Zbl LionsExistence of stationary states in Nonlinear scalar field equations. Bardos and D. Bessis eds. Lionswork in preparation. BergerOn the existence and structure of stationary states for a non-linear Klein-Gordon equation.

BonaD. Bose and R. TurnerFinite amplitude steady waves in stratified fluids.Lyophilization of Pharmaceuticals and Biologicals pp Cite as. The current chapter will address specific topics linked to high-concentration lyophilized protein formulations. We have therefore asked, how highly concentrated can a protein formulation become? We consider this question, particularly for monoclonal antibody drugs, along with the rationale for developing HCPF and the issues encountered during formulation.

Lyophilization is the technique of choice for stabilizing labile molecules. However, for the development of high-concentration, freeze-dried protein formulations HC-FDPFsnew challenges appear, such as extremely prolonged reconstitution times or even stability issues.

Therefore, new technologies such as controlled nucleation are introduced and presented as one option for reducing these unfavorable reconstitution times. Springer Nature is developing a new tool to find and evaluate Protocols.

Learn more. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Lyophilization of High-Concentration Protein Formulations. Protocol First Online: 19 December This is a preview of subscription content, log in to check access. Essig D Lyophilisation. Jennings TA Lyophilization. Wang W Lyophilization and development of solid protein pharmaceuticals.

Matejtschuk P Lyophilisation of proteins. Franks F, Auffret T Freeze-drying of pharmaceuticals and biopharmaceuticals. Principles and practice. Informa Heathcare, London, pp 1— Google Scholar. Varshney D, Singh M eds Lyophilised biologics and vaccines modality-based approaches.

Springer, New York, pp 1— Google Scholar. Wolkers WF, Oldenhof H eds Cryopreservation and freeze-drying protocols, methods in molecular biology, vol3rd edn. Frost GL Recombinant human hyaluronidase rHuPH20 : an enabling platform for subcutaneous drug and fluid administration.

Narasimhan C, Mach H, Shameen M High-dose monoclonal antibodies via the subcutaneouy route: challenges and technical solutions, an industry perspective. Leveque D Subcutaneous administration of anticancer agents.

Kling J Highly concentrated protein formulations. BioProcess Int 12 5 :2—11 Google Scholar. Gatlin LA, Gatlin CAB Formulation and administration techniques to minimize injection pain and tissue damage associated with parenteral products. Dias C, Abosaleem B, Crispino C, Cao B, Shaywitz A Tolerability of high-volume subcutaneous injections of a viscous placebo buffer: a randomized, crossover study in health subjects.BoxSouk Ahras, Algeria.

Concentration Compactness Alternatives

We discuss some compactness results in spaces related to the spectral theory of neutron transport equations for general classes of collision operators and Radon measures having velocity spaces as supports covering most physical models. We show in particular that the asymptotic spectrum of the transport operator is independent of. The Boltzmann equation is an integrodifferential equation of the kinetic theory which is devoted to the study of evolutionary behavior of the gas in the one particle phase space of position and velocity.

The time evolution of the state of a gas which is contained in a vessel bounded by solid walls is determined on one hand by the behavior of the gas molecules at collisions with each other and on the other hand by the influence of the walls as well as by external forces; in the case where there are no external forces, this state is described by a scalar function which models the density function of gas particles having position and velocity at time.

The integral of this function gives the expectation value statistical average of the total mass of gas contained in the phase space. Under some assumptions, function must satisfy the Boltzmann equation completed by boundary and initial conditions. The first term in is called streaming operator which is responsible for the motion of the particles between collisions, while the second onewhich is bilinear, describes the mechanism of collisions.

A solution to the initial boundary value problem for and a proof of -theorem are given by treating it under its abstract form for more details, see [ 1 ]. This equation is applied also to the transport of photons involved in studies of nuclear reactors, including calculations on the protection against radiation and calculations of warm-up of materials.

The quantum behavior of neutrons occurs in collisions with nuclei, but for physicists these events of collisions can be considered as one-time events and instantaneous, which only the consequences are interested in. According to the energy of the incident neutron and the nucleus with which it interacts, different types of reactions can occur.

The neutron can be absorbed or broadcasted or it causes the fission of the nucleus. Each reaction is characterized by the microscopic cross section. Between collisions, neutrons behave as classical particles, described by their position and speed. Uncharged neutral particlesthey move in a straight line at least for short distances for which we neglect the effect of the gravitation. The neutronic equations are naturally linear. Indeed, the neutron-neutron interactions can be neglected vis-a-vis neutron-matter interactions.

The relationship between the neutron density and the density of the propagation medium water, uranium oxyde, is of the orderwhich justifies this approximation. This assumption leads to simplifying the nonlinear version of the Boltzmann equation used in the kinetic theory of gases. Without delayed neutrons, these equations can be written under the form with initial datawhere.

The function describes the distribution of the neutrons in a nuclear reactor occupying the region. The functions and are called, respectively, the collision frequency and the scattering kernel. Here, the boundary conditions which represent the interaction between the particles and ambient medium are given by a boundary bounded operator satisfying where resp. The classical boundary conditions vacuum boundary, specular reflections, diffuse reflections, and periodic and mixed type boundary conditions are special examples of our framework.

We define the positive real numbers by Physically, is the time taken by a neutron initially in with animated speed to achieve for the first time the boundary of. We denote by the set where is the outer unit normal vector at. Let ; we introduce the functional spaces where The spaces of traces are. Here is the Lebesgue measure on. Recall that, for everywe can define the traces on ; unfortunately, these traces do not belong to.

The traces lie only in or precisely in a certain weighted space see [ 2 — 4 ], for details. Define In this case and the associated advection operator is given as follows: with domain where the collision frequency in other words, a positive bounded function.In addition, a byproduct is that the set of solutions is compact.

It arises in nonlinear quantum mechanics models and semiconductor theory. From a physical viewpoint, the system describes the interaction between identical charged particles, when the magnetic effects could be ignored in the interaction with each other and its solution is a standing wave for such a stationary system. The nonlinearity models the mutual interaction between many charged particles. The nonlocal term means that the particles interact with its own electric field.

For more information about the mathematical and physical background of the system, we refer the readers to see papers [ 1 — 4 ] and the references therein. See references [ 5 — 17 ] and the references therein. When the nonlinear term is presented as a subcritical growth, there are many results in the literature. Ruiz [ 18 ] studied the following system: where the parameter and. When is small, the author showed that there exists at least one positive radial solutions forand at least two positive radial solutions for.

Lions-type compactness and Rubik actions on the Heisenberg group

In particular, ifthe author proved that is a threshold of existence and nonexistence of positive radial solutions. When in system 2Azzollini and Pomponio [ 19 ] established the existence of ground state solution for.

Lecture 23(A): Compact Sets and Metric Spaces; Bolzano-Weierstrass Theorem

For related system and more results, please refer readers to see [ 20 — 28 ]. In the paper, we are concerned with a critical growth of nonlinearity term and perturbation of low order terms. In this case, there are some results in the references. As regards the following relevant system, where the parameter andunder some suitable conditions, existence of a nontrivial solution was proved in [ 19 ] for and in [ 29 ] for.

Here, we would like to mention some other papers [ 30 — 34 ] for related results. We note that the existence of solutions is very seriously depending on the range of the. Motivated by works mentioned above, particularly, by the results in [ 16242935 ], we overcome these difficulties mentioned above and obtain the existence of infinitely many negative energy solutions to system 1 for and small. We denote by the best constant for the Sobolev space imbedding into the Lebesgue spacenamely.

Theorem 1. Then, there exists a positive constant such that system 1 possesses infinitely many negative energy solutions for any. Moreover, the set of solutions obtained above is compact. Remark 2. To some extent, we extend the results in [ 16242935 ].

Infinitely Many Solutions of Schrödinger-Poisson Equations with Critical and Sublinear Terms

Remark 3. We followed the methods of Yao and Mu in [ 37 ], where the authors studied nonlocal problem of Kirchhoff-type in high dimension. The remainder of this paper is organized as follows.

In Section 2we present the abstract framework of the problem as well as some preliminary results. Theorem 1 shall be proved in Section 3. For anythe Lax-Milgram theorem implies that there exists a unique such that, for anythat is, is the weak solution of.

It is readily seen that the energy functional belongs to and that for any. Hence, if is a critical point of functionalthen is a solution of equation 10 and is a solution of system 1. We denote for simple expressions. Lemma 4. Lemma 5. Assume is a for functional in. Then, is bounded in.Moreover, we show that a minimizing problem, related to the existence of a ground state, has no solution. Unable to display preview. Download preview PDF.

Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Chapter First Online: 02 June This is a preview of subscription content, log in to check access. Ambrosetti, G. Cerami, D. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applicationsJ.

Azzollini, A. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinityNonlinear Anal.

Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionalsProc. Cerami, An existence criterion for the critical points on unbounded manifoldsItalian Istit. Lombardo Accad.

pp. 43–68. concentration and compactness arguments in

Ano. Google Scholar. Costa and C. Costa, H. Equations, — Jeanjean, K. Lehrer, L. Anal— Lions, The concentration-compactness principle in the calculus of variations.

The locally compact caseAnn. Maia and R. Silva, Subharmonic solutions for subquadratic Hamiltonian systemsJ. Equations— Spradlin, Existence of solutions to a hamiltonian System without convexity condition on the nonlinearityElect.

Spradlin, Interacting near-solutions of a hamiltonian systemCalc. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearitiesMath.

pp. 43–68. concentration and compactness arguments in

Stuart and H. Partial Diff.Defining the covariant derivative. The system has two important features. First, it enjoys the gauge invariance. Second, it is Lorentz invariant. Moreover, the system admits a conserved energy.

Given that the system of equations 1. The most advanced results for large data can be achieved for critical equations. More precisely, we implement an analysis closely analogous to the one by the first author and Schlag [ 20 ] in the context of critical wave maps in order to prove existence, scattering and a priori bounds for large global solutions to MKG-CG.

One can easily verify that as long as the solution exists in the sense of [ 36 ], and hence in the smooth sense, it will be admissible on fixed time slices. The above notion of admissible data therefore leads to a natural concept of solution to work with, and we call such solutions admissible. Our main theorem can then be stated as follows. There exists a function. The purpose of this norm is to control the regularity of the solutions. Recently, a proof of the global regularity and scattering affirmations in the preceding theorem was obtained by Oh-Tataru [ 32 — 34 ], following the method developed by Sterbenz-Tataru [ 4041 ] in the context of critical wave maps.

Our conclusions were reached before the appearance of their work and our methods are completely independent. In this subsection we first consider this work in the broader context of the study of the local and global in time behavior of nonlinear wave equations and highlight some of the important developments over the last decades that crucially enter the proof of our main theorem.

Afterwards we give an overview of previous results on the Maxwell-Klein-Gordon equation. Null structure. In many geometric wave equations like the wave map equation, the Maxwell-Klein-Gordon equation, and the Yang-Mills equation, the nonlinearities exhibit so-called null structures.

Heuristically speaking, such null structures are amenable to better estimates, because they damp the interactions of parallel waves.

Pp. 43–68. concentration and compactness arguments in