A general model for the absorption of ultrasound by biological tissues and experimental verification

In this paper, a closed-form expression is derived for the absorption of ultrasound by biological tissues. In this expression, the viscothermal and viscoelastic theories of relaxation processes are combined. Three relaxation time distribution functions are introduced, and it is assumed that each of these distributions can be described by an identical and simple hyperbolic function. Several simplifying assumptions had to be made to enable the experimental verification of the derived closed-form expression of the absorption coefficient. The simplified expression leaves two degrees of freedom and it was fitted to the experimental data obtained from homogenized beef liver. The model produced a considerably better fit to the data than other, more pragmatic models for the absorption coefficient as a function of frequency that could be found in the literature. Scattering in beef liver was estimated indirectly from the difference between attenuation in in vitro liver tissue as compared to absorption in a homogenate. The frequency dependence of the scattering coefficient could be described by a power law with a power of the order of 2. A comparable figure was found in direct backscattering measurements, performed at our laboratory with the same liver samples [Van den Aarssen et al., J. Acoust. Soc. Am. (to be published)]. A model for scattering recently proposed by Sehgal and Greenleaf [Ultrason. Imag. 6, 60-80 (1984)] was fitted to the scattering data as well. This latter model enabled the estimation of a maximum scatterer distance, which appeared to be of the order of 25 micron.     

On Absorbing Cycles in Min–Max Digraphs

We consider smooth finite dimensional optimization problems with a compact, connected feasible set M and objective function f. The basic problem, on which we focus, is: how to get from one local minimum to all the other ones. To this aim we introduce a bipartite digraph as follows. Its nodes are formed by the set of local minima and maxima of f|_M, respectively. Given a smooth Riemannian (i.e. variable) metric, there is an arc from a local minimum x to a local maximum y if the ascent (semi-)flow induced by the projected gradients of f connects points from a neighborhood of x with points from a neighborhood of y. The existence of an arc from y to x is defined with the aid of the descent (semi-)flow. Strong connectedness of ensures that, starting from one local minimum, we may reach any other one using ascent and descent trajectories in an alternating way. In case that no inequality constraints are present or active, it is well known that for a generic Riemannian metric the resulting min-max digraph is indeed strongly connected. However, if inequality constraints are active, then there might appear obstructions. In fact, we show that may contain absorbing two-cycles. If one enters such a cycle, one cannot leave it anymore via ascent and descent trajectories. Moreover, the cycles being constructed are stable with respect to small perturbations (in the C¹-topology) of the Riemannian metric.     

Structure and mesomorphism of neodymium(III) alkanoates

The structural and thermal behavior of all members of the homologous series of neodymium(III) alkanoates, ranging from neodymium(III) butyrate to neodymium(III) eicosanoate are described. Neodymium(III) butyrate monohydrate, Nd(C3H7COO)3.H2O crystallizes in space group P1 (No. 2), Z = 2. The lattice parameters are a = 9.824(2) A, b = 11.974(2) A, c = 14.633(2) A, alpha = 86.21(2) degrees, beta = 75.92(2) degrees, gamma = 77.97(2) degrees. The crystal structure consists of ionic layers of neodymium ions, separated by bilayers of butyrate anions. In the ionic layers, the neodymium ions are connected by bridging tridentate carboxylate groups to zigzag chains, whereas the chains are connected among themselves by bridging bidentate carboxylate groups. The two crystallographically different neodymium ions are both having coordination number 9, with a geometry close to a monocapped square antiprism. The structure of the higher homologues can be derived from the structure of neodymium butyrate by extending the alkyl chains. These compounds have a lamellar bilayer structure with planes of neodymium(III) ions coordinated to the carboxylate groups and with the alkyl chains in an all-trans conformation. All homologous compounds from neodymium(III) pentanoate to neodymium(III) pentadecanoate display a thermotropic mesophase, which was identified by high-temperature X-ray diffraction as a smectic A phase. For the series from neodymium(III) pentanoate to neodymium(III) undecanoate an additional high viscosity mesophase is present between the crystalline state and the smectic A mesophase.     

Nonlinear optimization: Characterization of structural stability

We study global stability properties for differentiable optimization problems of the type: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbGaai% ikaGqaaiaa-jzacaGGSaGaamisaiaacYcacaqGGaGaam4raiaacMca% caGG6aGaaeiiaiaab2eacaqGPbGaaeOBaiaabccacaWFsgGaaeikai% aadIhacaqGPaGaaeiiaiaab+gacaqGUbGaaeiiaiaad2eacaGGBbGa% amisaiaacYcacaWGhbGaaiyxaiabg2da9iaacUhacaWG4bGaeyicI4% CeeuuDJXwAKbsr4rNCHbacfaGae4xhHe6aaWbaaSqabeaacaWGUbaa% aOGaaiiFaiaabccacaWGibGaaiikaiaadIhacaGGPaGaeyypa0JaaG% imaiaacYcacaqGGaGaam4raiaacIcacaWG4bGaaiykamaamaaabaGa% eyyzImlaaiaaicdacaGG9bGaaiOlaaaa!6B2E!\[P(f,H,{\text{ }}G):{\text{ Min }}f{\text{(}}x{\text{) on }}M[H,G] = \{ x \in \mathbb{R}^n |{\text{ }}H(x) = 0,{\text{ }}G(x)\underline \geqslant 0\} .\] Two problems are called equivalent if each lower level set of one problem is mapped homeomorphically onto a corresponding lower level set of the other one. In case that P(% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaaceWFsg% GbaGaacaWFSaGaa8hiaiqadIeagaacaiaacYcacaWFGaGabm4rayaa% iaaaaa!3EBF!\[\tilde f, \tilde H, \tilde G\]) is equivalent with P(f, H, GG) for all (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaieaaceWFsg% GbaGaacaWFSaGaa8hiaiqadIeagaacaiaacYcacaWFGaGabm4rayaa% iaaaaa!3EBF!\[\tilde f, \tilde H, \tilde G\]) in some neighbourhood of (f, H, G) we call P(f, H, G) structurally stable; the topology used takes derivatives up to order two into account. Under the assumption that M[H, G] is compact we prove that structural stability of P(f, H, GG) is equivalent with the validity of the following three conditions:

1. The Mangasarian-Fromovitz constraint qualification is satisfied at every point of M[H, G].
2. Every Kuhn-Tucker point of P(f, H, GG) is strongly stable in the sense of Kojima.
3. Different Kuhn-Tucker points have different (f-)values.

     

Use of seeds to control precipitation of calcium carbonate and determination of seed nature

Understanding and controlling precipitation reactions is a major challenge for industrial crystallization. Calcium carbonate is a widely studied system: more than 3000 papers have been devoted to the subject over the past 10 years. The first step of the precipitation of calcium carbonate, from relatively concentrated solutions (0.01 mol/L), involves the formation of an initial gel phase which later transforms into calcite, vaterite, or a mixture of both phases. Our work aimed at controlling this first step. Nanosized seeds (8 nm), formed in situ, were used in order to control the often chaotic nucleation step which normally leads to poor phase selection and broad particle size distributions. Seeding has often been used to avoid spontaneous nucleation in metastable solutions for growth mechanism investigations of single-crystal calcium carbonate. Here the ability of a seeding method to control the precipitation reaction evolution even in the case of high supersaturation is demonstrated. The seeds and the presence of a polymeric additive (poly(acrylic acid)) allow the control of the precipitated polymorph and the specific surface area, while maintaining a narrow particle size distribution in the submicron range. Direct characterization methods did not succeed in identifying these nanoseeds; indirect methods using solubility calculations are used to demonstrate their existence and quantify size and number density of the nanosized seeds.     

Surface hydroxylation of poly(vinylidene fluoride) (PVDF) film

The surface of PVDF film was selectively modified by wet chemistry. Treatment with aqueous LiOH produced HF-elimination and the emergence of an oxygen-containing functionality. The XPS analysis clearly indicated the presence of ketone-, ether(epoxide)-, and alcohol motifs. The percentage of alcohols could be significantly increased by reduction of the ketones with NaBH₄ in 2-propanol, followed by reduction of the epoxides with DIBAL-H in hexane. Thus, the full treatment led to a PVDF surface displaying 7 to 16% of oxygen-containing units, of which about 60% consisted in alcohol motifs. The reactvity of the surface-displayed hydroxyl functions was assayed by radiolabeling with [³H]-Ac₂O. © 1997 John Wiley & Sons, Inc. J. Polym Sci A: Polym Chem 35: 1227–1235, 1997     

Global Optimization: Local Minima and Transition Points

We consider the minimization of smooth functions of the Euclidean space with a finite number of stationary points having moderate asymptotic behavior at infinity. The crucial role of transition points of first order (i.e., saddle points of index 1) is emphasized. It is shown that (generically) any two local minima can be connected via an alternating sequence of local minima and transition points of first order. In particular, the graph with local minima as its nodes and first order transition points representing the edges turns out to be connected (Theorem A). On the other hand, any connected (finite) graph can be realized in the above sense by means of a smooth function of three variables having a minimal number of stationary points (Theorem B).     

Criteria for efficiency in vector optimization

We consider unconstrained finite dimensional multi-criteria optimization problems, where the objective functions are continuously differentiable. Motivated by previous work of Brosowski and da Silva (1994), we suggest a number of tests (TEST 1–4) to detect, whether a certain point is a locally (weakly) efficient solution for the underlying vector optimization problem or not. Our aim is to show: the points, at which none of the TESTs 1–4 can be applied, form a nowhere dense set in the state space. TESTs 1 and 2 are exactly those proposed by Brosowski and da Silva. TEST 3 deals with a local constant behavior of at least one of the objective functions. TEST 4 includes some conditions on the gradients of objective functions satisfied locally around the point of interest. It is formulated as a Conjecture. It is proven under additional assumptions on the objective functions, such as linear independence of the gradients, convexity or directional monotonicity. This work was partially supported by grant 55681 of the CONACyT.     

Effect of the magnetic field from the accelerating system on the beam dynamics in the cyclotron

Magnetic components of the HF field in a cyclotron can change the transverse beam size and the phase width of bunches during acceleration. As a consequence, the phase portraits of the beam at the entrance to the electrostatic deflector and thus the efficiency of the extraction system can change. Expressions are obtained for the components of the magnetic field from the HF system in the vicinity of the cyclotron median plane. The effect of this field on the beam parameters during acceleration and at the entrance to the electrostatic deflector is shown by numerical simulation. For the C235 proton cyclotron, the beam parameter variation is as large as 50%.