19,367 research outputs found

    On polyhedral approximations of the positive semidefinite cone

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    Let DD be the set of n×nn\times n positive semidefinite matrices of trace equal to one, also known as the set of density matrices. We prove two results on the hardness of approximating DD with polytopes. First, we show that if 0<Ï”<10 < \epsilon < 1 and AA is an arbitrary matrix of trace equal to one, any polytope PP such that (1−ϔ)(D−A)⊂P⊂D−A(1-\epsilon)(D-A) \subset P \subset D-A must have linear programming extension complexity at least exp⁥(cn)\exp(c\sqrt{n}) where c>0c > 0 is a constant that depends on Ï”\epsilon. Second, we show that any polytope PP such that D⊂PD \subset P and such that the Gaussian width of PP is at most twice the Gaussian width of DD must have extension complexity at least exp⁥(cn1/3)\exp(cn^{1/3}). The main ingredient of our proofs is hypercontractivity of the noise operator on the hypercube.Comment: 12 page

    LANGUAGE MAINTENANCE AND LANGUAGE SHIFT

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    In language shifts, ancestral tongues are abandoned by their speakers and replaced, in one way or another, by dominant languages. Such changes in language use will ultimately lead to the irreversible suppression of the world's language diversity. Language maintenance attempts to counter these processes. Linguists may assist ethno linguistic minorities in safeguarding their threatened languages in many different ways, including establishing orthography when necessary, but speakers decide to abandon their heritage languages within a broad socio-political and economic context. Communities uphold or give up languages, so only the speakers of endangered languages themselves can opt for and execute language maintenance activities. Linguists might have to accept that some communities may no longer care for their heritage languages

    Patterns and motivations predicting mobile hard news and soft news consumption: The case of the UAE

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    The purpose of this study is to examine Emirati university students\u27 usage of smartphones as a news resource. In addition to the motivations, patterns, and relationships between hard news and soft news consumption and the different gratifications sought, this study adopted perspectives from the both the uses and gratifications and media displacement theories and utilized a quantitative research design. Data was collected from 488 undergraduate students between February 2019 and March 2019. Results revealed that students were interested in both hard and soft news, but there was 7% more soft news consumption by students. Additionally, results revealed that smartphones have become students\u27 main source of news as they allow them to find information easily. When assessing the relationships and dynamics between mobile news and the gratifications sought, results revealed that the convenience gratification was the only predictor of both mobile soft news and hard news out of all the gratifications offered

    Monetary-Exchange Rate Policy and Current Account Dynamics

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    A dynamic stochastic general equilibrium monetary model with incomplete and imperfect asset markets, monopolistic competition and staggered nominal price rigidities is developed to shed light on the role of exchange rate and its relation with current account dynamics in the formulation of monetary-exchange rate policies. The paper shows that because of incomplete risk sharing, due to incomplete asset markets, the dynamic relationship between real exchange rate and net foreign assets affect the behaviour of domestic inflation and aggregate output. This, in turn, implies that the optimal monetary policy entail a response to net foreign asset position or the real exchange rate gap defined as the difference between actual real exchange rate and the value that would prevail with flexible prices and complete asset markets. In comparing the performance of alternative monetary-exchange rate policy rules, an interesting and fairly robust result that stands out is that ‘dirty floating’ out-performs flexible exchange rate regime with domestic inflation targeting.optimal monetary policy; incomplete asset markets; net foreign assets; current account dynamics; inflation targeting; exchange rate policy

    EMPLOYEE STOCK OPTIONS INCENTIVE EFFECTS: A CPT-BASED MODEL

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    This paper examines the incentives from stock options for loss-averse employees subject to probability weighting. Employing the certainty equivalence principle, I built on insights from Cumulative Prospect Theory (CPT) to derive a continuous time model to value options from the perspective of a representative employee. Consistent with a growing body of empirical and experimental studies, the model predicts that the employee may overestimate the value of his options in-excess of their risk-neutral value. This is nevertheless in stark contrast with a common finding of standard models based on the Expected Utility Theory (EUT) framework that options value to a risk-averse undiversified employee is strictly lower than the value to risk-neutral outside investors. In particular, I proved that loss aversion and probability weighting have countervailing effects on the option subjective value. In addition, for typical setting of preferences parameters around the experimental estimates, and assuming the company is allowed to adjust existing compensation when making new stock option grants, the model predicts that incentives are maximized for strike prices set around the stock price at inception. This finding is consistent with companies' actual compensation practices that standard EUT-based models have difficulties accommodating their existence.Stock options, Cumulative Prospect Theory, Incentives, Subjective value

    STUDIES ON HIGH-PERFORMANCE THERMOSETS AND THEIR INTERFACE AND INTERPHASE WITH CARBON-NANOTUBES

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    Materials with higher strength to weight ratio than the current state of the art (SOA) carbon fiber reinforced plastics (CFRP) are desired by NASA to support affordable space exploration, including human travel to mars and beyond. The carbon nanotube-polymer (CNT-polymer) composites are expected to have significantly better mechanical properties than the current SOA CFRP and qualify as a potential system for achieving the target mechanical properties in materials required to support human travel to mars. CNT containing polymer composites, however, have some limitations, one of which is the load transfer at the CNT- polymer interface. The interface plays a critical role in determining the overall macroscale properties of the composite. While, significant attention has been directed to this end the CNTs in the composites have not yet reached their full potential. There are several aspects of the CNT-polymer composites which can help create the next generation of high strength and lightweight materials, to help support human travel to mars and beyond. These include, (a) improving the fracture toughness of the polymer resin, (b) understanding and optimizing the CNT-polymer interactions, (c) understanding the effects of CNTs on the polymer cure reactions, which consequently can alter the mechanical properties of the composite, (d) modifying the CNT-polymer interface-interphase through surface treatment and sizing, (e) understanding the effects of amorphous carbon on the CNT-polymer interface-interphase. Herein, the first part of the dissertation focuses on the effect of processing on the molecular structure and the properties of a multi-component aerospace grade bismaleimide (BMI) resin, containing no CNTs, and is discussed in Chapter 2. Materials in nature such as nacre that are made of mechanically inferior building blocks exhibit extreme toughness at the macro scale because of the geometry and arrangement of their constituents. Taking a cue from these systems, we have investigated whether the molecular rearrangement in a heterogeneous BMI system can alter toughness at the macro scale. To this end, a multicomponent BMI system is processed by using (a) a melt and cast (termed Melt) approach and (b) a dual asymmetric centrifuge based high-speed shear mixing (termed HSSM) approach to enforce molecular rearrangement. FTIR, Raman, and NMR spectroscopies have been used to study the molecular rearrangement upon HSSM processing. Small-angle X-ray scattering has been used to study the effect of processing on the molecular arrangement of the BMI. The second part of this dissertation focuses on the structure, process and properties of CNT modified BMI, with tailored interface-interphase and is discussed in Chapter 3. With the recent large-scale production and availability of the CNT macro-assemblies in the yarn, tape and sheet forms, CNT-polymer composites could now be prepared through conventional CFRP manufacturing techniques such as filament winding. It is however expected that the resin dominated properties, such as the inter and intra laminar fracture toughness in these CNT- polymer composites would still remain relatively weak, as they have been for the CFRPs. Modifying the resin with CNTs is an attractive route for further improving the resin properties. Herein, CNT- BMI nanocomposites using three different CNTs and via two different processing routes, have been prepared and studied. The third part of this dissertation focuses on the effects that the CNT have on the cure of the BMI, as well as the effects that the cure of BMI has on the CNTs, in the nanocomposites containing up to 40 wt% CNTs, and is discussed in Chapter 4. CNTs can interact with the BMI system through the NH-π, π-π, CH-π, and OH-π, non-covalent interactions. The individual components of the BMI however can have exclusive non-covalent interactions with the CNTs. For example, in a BMI system containing 4,4'- bismaleimidodiphenylmethane (BDM) and diallylbisphenol A (DABA) components, only the BDM component contains the maleimide functional group which can potentially interact with the CNTs through the NH-π bonding, while only the DABA component, containing the OH functional group can potentially interact with the CNTs through the OH-π interactions. The potential for the preferential stacking of the different BMI components around the CNTs, can have important implications on the cure behavior of the BMI in the nanocomposite and consequently on the overall mechanical properties of the nanocomposite. Herein, two different types of CNTs in the sheet form: unbaked and baked (termed as UB and B CNT), have been employed. The effects of the varying CNT content on the inter-CNT spacing, cure reactions of the BMI, compression of CNTs and the thermomechanical properties of the nanocomposites have been investigated. The thermomechanical results and the theoretical calculations have then been used to estimate the interphase thickness of the CNT- BMI nanocomposites. The fourth part of this dissertation focuses on sizing and tailoring the CNT- BMI interface - interphase using a carbon fiber sizing, and is discussed in Chapter 5. Sizing of carbon and glass fibers is a critical step in the manufacturing of their respective composites with polymers and has led to improved interfacial shear strength (IFSS), inter-laminar shear strength (ILSS) and fracture toughness of the composites. As the CNT-polymer composites could now be prepared through conventional CFRP manufacturing techniques such as filament winding, the question is, could we integrate another critical step of the conventional CFRP manufacturing, i.e., ‘sizing’, to the CNT-polymer composite preparation to tailor the CNT-polymer interface-interphase? To be able to answer that question, we first need to understand the sizing-CNT interactions and reactions. To this end, herein, the effects that (a) CNTs, (b) the degree of functionalization and defects (DOFD) in the CNTs and (c) the sizing content, have on the sizing cure reaction and cure kinetics have been evaluated. CNTs with three different DOFD have been employed. The sizing coated CNTs have then been used to prepare nanocomposite films with a high- performance aerospace grade bismaleimide (BMI) resin. Overall three different types of CNT- BMI interface-interphase have been prepared and studied in nanocomposites containing 60 wt% CNTs: (a) pristine CNT- BMI, (b) functionalized CNT- BMI, and (c) sizing coated functionalized CNT- BMI. The effect of CNT, CNT functionalization and sizing coated CNTs on the BMI cure reactions, thermomechanical properties and the molecular heterogeneity and hierarchy of the nanocomposites have been studied and discussed. Finally, CNTs may contain amorphous carbon, among other impurities which consequently could interfere with the interfacial interactions of the CNT and the polymer. While such impurities are expected to have a negative effect on the polymer-CNT interface, quantitative evidence of the extent of such negative effects is lacking. Herein, the effect that the amorphous carbon and the baking of CNTs to remove the amorphous carbon have, on the interfacial stress transfer with the polyurea matrix has been studied and discussed in Chapter 6. During CNT synthesis, by products such as amorphous carbon may be formed which consequently could interfere with the interfacial interactions of the CNT and the polymer. While such impurities are expected to have a negative effect on the polymer-CNT interface, quantitative evidence of the extent of such negative effects is lacking. Herein, the difference in interfacial straining has been studied in composites of polyurea with two types of CNT sheets: (a) sheets containing amorphous carbon (termed as unbaked CNT sheet) and (b) sheets that are thermally treated to remove amorphous carbon (termed as baked CNT sheet). The understanding of the effects of the amorphous carbon and the baking treatment, based on the CNT- polyurea system should be translatable to other CNT-polymer system, including the CNT-BMI system. It is expected that these studies will provide guidance for the manufacturing of CNT, or CNT and carbon fiber hybrid based laminates that will ultimately meet NASA mechanical property goals.Ph.D

    Crashworthiness capability of jute and glass fibre reinforced epoxy tubes under quasi-static loading condition for automotive application

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    During last few years, the interest in using natural fibers as reinforcement in polymers has increased dramatically. Natural fibers are not only strong and lightweight but also relatively very cheap. This study examined the potential utilization of jute in the crash energy absorption. A combination of hand layup and vacuum bladder technique was kused to search the influence of utilizing jute fibre on crashworthiness parameters of composite materials. To improve the mechanical properties, jute fiber was hybridized with glass fiber. In this work, there are two main parts of study. Firstly, it is to investigate the effect of cross-sectional shapes, number of layers and temperature treatment on the progressive deformation of jute/epoxy composite tubes. Secondly, the suitable type of geometry was chosen to study the effect of hybrid (jute-glass/epoxy) onto the structural designs. All the tests were undergone quasi-static axial crushing of 10 mm/min. Their peak load (Pmax), mean load (Pm), energy absorption (EA) and specific energy absorption (SEA) were discussed in detail. In the study of types of five geometrical shapes (corrugated, circular, hexagonal, octagonal and decagonal cross sectional) with different number of layers (two, three and four layers). It is found that the corrugated geometric shape with three layers (RHS) gives the best energy absorption (30.92 J/g) in specific energy absorption parameter compared to other geometries used in present study. For the temperature treatment, the results showed that the post-curing by gradual temperature treatment (TT) improved the peak load by decreased with 55% as compared to similar circular specimen without temperature treatment (No TT). From the test, it is found that the substitution of one layer of jute fibre with one layer of glass fibre resulted in an improvement in the crashworthiness parameters than layers jute. The best result was obtained when hybrid jute-glass was used, where the energy absorption and specific energy absorption was improved by about 43% and 31%, respectively
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