Backward Stochastic Riccati Equations and Infinite Horizon L-Q Optimal Control with Infinite Dimensional State Space and Random Coefficients

We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random. In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed.     

Studies of poly(vinylidene fluoride)/poly(vinyl pyrrolidone) blends. I. Thermal transitions by differential scanning calorimetry

Thermal measurements were carried out to investigate the macrostructure of as-cast poly(vinylidene fluoride) (PVDF)/poly(vinyl pyrrolidone) (PVP) blends. At high PVP content, above about 70 wt.%, the two components form a homogeneously mixed amorphous phase whose T_g varies with composition. Crystals are formed upon casting mixtures richer in PVDF; these systems exhibit complex thermal behavior that cannot be justified by a simple two-phase model. DSC measurements above room temperature on semicrystalline blends show, in addition to the melting of PVDF crystals at temperatures that decrease on increasing PVP content, a glass transition at about 80°C, independent of composition. Experimental results strongly support the hypothesis that an interphase, composed of essentially undiluted noncrystalline PVDF, is always associated with the lamellar crystals.     

Preparing Pre‐Service Teachers to Teach Mathematics in Inclusive Classrooms: A Three‐Year Case Study

Federal and state regulations mandating inclusion of students with disabilities in general education classes have made it essential to create pathways for pre‐service teachers to develop skills to teach content to diverse groups of students. The study uses a framework suggested by the relationship between teacher attitude and teacher behavior ( Fullan, 1982 ), teacher beliefs and practice, and self‐efficacy and behavioral change ( Bandura, 1977 ). The purpose of the study was to examine changes, if any, in three cohorts of general education teacher candidates' (n=13, n=8, n=5) attitudes toward teaching mathematics to students with disabilities after participating in focused instructional experiences which provided both information and vicarious positive teaching activities in special education. Data collected included pretest and posttest scores for each of the three cohorts and journal entries. Little or no change in attitude towards students with disabilities and mathematics, and efficacy to teach students with disabilities was observed for the year one and year two cohorts. In the third year the modules were combined with a structured field experience. The data collected from the third year cohort suggested a positive trend in attitude as measured by the survey data and field experience journal data. Future study with larger samples is needed.     

Thermodynamics of alcohols and monosaccharides in aqueous solutions of thiourea at 25°C

The excess enthalpies of twelve ternary aqueous solutions of alcohols or monosaccharides containing thiourea have been determined by flow microcalorimetry at 25°C. The coefficients of the virial expansion of the excess enthalpies are compared with those reported in the literature for the same ternary solutions containing urea in place of thiourea. The cross-interaction coefficients are positive for the thiourea-alcohol systems and depend on the length and branching of the alkyl chain of the alcohols. On the other hand, they are negative for the thiourea-monosaccharide systems. Thus, thiourea, as urea, can be used as a probe to reveal differences in the behavior of families of solutes characterized by the same functional groups. The results can be interpreted in terms of the relative stabilities of hydration cospheres of hydrophobic or hydrophilic solutes toward a chaotropic agent such as thiourea.Presented at the sixth Italian meeting on Calorimetry and Thermal Analysis (AICAT) held in Naples, December 4–7, 1984.     

High quantum yield photoluminescence of new polyamides containing oligo‐PPV amino derivatives and related oligomers

The synthesis and the chemical physical characterization of new photoluminescent (PL) chromophores and polymers are reported. Chromophores (oligo‐PPV symmetric derivatives ending with amino groups) are strong blue emitters with a PL quantum yield of ～70% in dioxane solution. They have been used to prepare polyamides by reaction with aliphatic acyl dichlorides in which emitting and non emitting units are alternated. PL properties of the synthesized polyamides have been evaluated in solution and reveal a strong blue emission (PL quantum yield ～60%), To increase the solubility of these systems, oligomers have been purposely prepared and then characterized. They show a peculiar white emission when excited in DMF solution; to get insight into this interesting behavior, asymmetric monoacetylated chromophores have been prepared as model compounds for the chromophoric end groups of the polyamide chains. The emission spectra of these compounds reveal a broad excimeric yellow emission which is responsible, along with the blue emission of the inner chromophoric units, of the overall white emission of the oligomers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2677–2689, 2009     

Radicals in skew polynomial and skew Laurent polynomial rings

We provide a general procedure for characterizing radical-like functions of skew polynomial and skew Laurent polynomial rings under grading hypotheses. In particular, we are able to completely characterize the Wedderburn and Levitzki radicals of skew polynomial and skew Laurent polynomial rings in terms of ideals in the coefficient ring. We also introduce the T-nilpotent radideals, and perform similar characterizations.     

3-Nets realizing a group in a projective plane

In a projective plane $\mathit{PG}(2,\mathbb{K})$ defined over an algebraically closed field $\mathbb{K}$ of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614–1624, 2004), arises from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv. Math. 219:672–688, 2008), comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzúa’s 3-nets (Adv. Geom. 10:287–310, 2010) realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds in characteristic p>0 apart from three possible exceptions $\rm{Alt}_{4}$ , $\rm{Sym}_{4}$ , and $\rm{Alt}_{5}$ . Motivation for the study of finite 3-nets in the complex plane comes from the study of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky in Compos. Math. 143:1069–1088, 2007; Miguel and Buzunáriz in Graphs Comb. 25:469–488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672–688, 2008; Yuzvinsky in Compos. Math. 140:1614–1624, 2004; Yuzvinsky in Proc. Am. Math. Soc. 137:1641–1648, 2009).