Proof of the Double Bubble Conjecture in R^n

The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble.Comment: 20 pages, 22 figure

On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.Comment: 27 pages; Accepted Manuscrip

Using a Mark-to-Market Valuation Technique to Objectively Measure IT Portfolio Value Creation

Enterprise executives frequently face the challenge of making decisions under conditions of significant uncertainty when dealing with IT investments, IT project management and realization of intangible organizational benefits enabled by IT. A suitable methodology for accurately estimating the current financial standing of each project in a portfolio of IT projects over the full project lifecycle is useful for IT managers to understand IT value creation and manage the IT projects across the portfolio. In line with this perspective, we propose a Mark-to-Market valuation technique that enables a standardized approach across diverse IT projects that comprise the IT portfolio. Three main contributions may be drawn from this study: 1) the Mark-to-Market approach is a useful valuation technique in the context of IT projects; 2) practitioners may leverage the technique to assess project value and the performance of the IT portfolio over the lifecycle of such projects; and 3) the consistent treatment of each project allows aggregation and applications of standard portfolio management techniques to the practice of IT portfolio management

Enhanced thermal stability and fracture toughness of TiAlN coatings by Cr, Nb and V-alloying

The effect of metal alloying on mechanical properties including hardness and fracture toughness were investigated in three alloys, Ti~0.33Al0.50(Me)~0.17N (Me¿=¿Cr, Nb and V), and compared to Ti0.50Al0.50N, in the as-deposited state and after annealing. All studied alloys display similar as-deposited hardness while the hardness evolution during annealing is found to be connected to phase transformations, related to the alloy's thermal stability. The most pronounced hardening was observed in Ti0.50Al0.50N, while all the coatings with additional metal elements sustain their hardness better and they are harder than Ti0.50Al0.50N after annealing at 1100¿°C. Fracture toughness properties were extracted from scratch tests. In all tested conditions, as-deposited and annealed at 900 and 1100¿°C, Ti0.33Al0.50Nb0.17N show the least surface and sub-surface damage when scratched despite the differences in decomposition behavior and h-AlN formation. Theoretically estimated ductility of phases existing in the coatings correlates well with their crack resistance. In summary, Ti0.33Al0.50Nb0.17N is the toughest alloy in both as-deposited and post-annealed states.Peer ReviewedPostprint (author's final draft

Next-to-leading-order corrections to exclusive processes in kTk_T factorization

We calculate next-to-leading-order (NLO) corrections to exclusive processes in $k_T$ factorization theorem, taking $\pi\gamma^*\to\gamma$ as an example. Partons off-shell by $k_T^2$ are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the $k_T$-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the $k_T$-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms $\ln^2k_T$ and $\ln^2 x$, $x$ being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the $k_T$ resummation, and the latter absorbed into a jet function and organized by the threshold resummation. The NLO corrections are found to be only few-percent for $\pi\gamma^*\to\gamma$, if setting the factorization scale to the momentum transfer from the virtual photon.Comment: 13 pages; version to appear in Physical Review

Pole Assignment for a Vibrating System with Aerodynamic Effect

This paper deals with a pole assignment problem by single-input state feedback control arising from a one-dimensional vibrating system with aerodynamic effect. On the practical side, we derive explicit formulae for the required controlling force terms, which can reassign part of the spectrum to the desired values while leaving the remaining spectrum unchanged. On the mathematical side, unlike the classical Sturm–Liouville problem, our eigenvalue problem is associated with a cubic pencil with unbounded operators as coefficients and has many interesting new features, one of which is that a new controllability condition appears. This condition together with the known controllability condition in the quadratic case are necessary and sufficient. This sheds light on the adjustment of the model parameters. We also analyze the spectrum of the associated noncompact operator and in particular show that the discrete spectrums of controlled and uncontrolled systems lie outside a closed interval on the negative real axis

Extraction of VubV_{ub} from the Decay B→πlνB\to \pi l \nu

We develop the perturbative QCD formalism including Sudakov effects for semi-leptonic $B$ meson decays. We evaluate the differential decay rate of $B\to \pi l \nu$, and find that the perturbative calculation is reliable for the energy fraction of the pion above 0.3. Combining predictions from the soft pion theorems, we extract the value of the matrix element $|V_{ub}|$ which is roughly $2.7\times 10^{-3}$.Comment: 10 pages, CCUTH-94-05, IP-ASTP-13-9

Impact of Six Genetic Modifications of Corn on Feed Cost and the Consumption of Traditional Feed Ingredients

There is excitement about the potential profit and economic development opportunities from genetic modifications of grain. This excitement is manifested in huge industry consolidations through buyouts, joint ventures, and mergers of chemical, seed and agribusiness companies. State and federal government agencies and private organizations have developed programs to encourage and facilitate the production, handling, processing, and marketing of genetically modified grains. Huge investments are being allocated to research and development of new commodities and specialty grains. A large share of these research and development funds are being invested in modifying com because of the large amount of com produced in the United States and its diversity of uses. About 80 percent of the U.S. corn crop is used in animal feeds domestically and abroad; therefore, genetic modifications of com for animal feed are believed to have major profit and development potential

Long-Term and Global Tradeoffs between Bio-Energy, Feed, and Food

Projections of U.S. ethanol production and its impacts on planted acreage, crop prices, livestock production and prices, trade, and retail food costs are presented under the assumption that current tax credits and trade policies are maintained. The projections were made using a multi-product, multi-country deterministic partial equilibrium model. The impacts of higher oil prices, a drought combined with an ethanol mandate, and removal of land from the Conservation Reserve Program (CRP) relative to baseline projections are also presented. The results indicate that expanded U.S. ethanol production will cause long-run crop prices to increase. In response to higher feed costs, livestock farmgate prices will increase enough to cover the feed cost increases. Retail meat, egg, and dairy prices will also increase. If oil prices are permanently $10-per-barrel higher than assumed in the baseline projections, U.S. ethanol will expand significantly. The magnitude of the expansion will depend on the future makeup of the U.S. automobile fleet. If sufficient demand for E-85 from flex-fuel vehicles is available, corn-based ethanol production is projected to increase to over 30 billion gallons per year with the higher oil prices. The direct effect of higher feed costs is that U.S. food prices would increase by a minimum of 1.1% over baseline levels. Results of a model of a 1988-type drought combined with a large mandate for continued ethanol production show sharply higher crop prices, a drop in livestock production, and higher food prices. Corn exports would drop significantly, and feed costs would rise. Wheat feed use would rise sharply. Taking additional land out of the CRP would lower crop prices in the short run. But because long-run corn prices are determined by ethanol prices and not by corn acreage, the long-run impacts on commodity prices and food prices of a smaller CRP are modest. Cellulosic ethanol from switchgrass and biodiesel from soybeans do not become economically viable in the Corn Belt under any of the scenarios. This is so because high energy costs that increase the prices of biodiesel and switchgrass ethanol also increase the price of corn-based ethanol. So long as producers can choose between soybeans for biodiesel, switchgrass for ethanol, and corn for ethanol, they will choose to grow corn. Cellulosic ethanol from corn stover does not enter into any scenario because of the high cost of collecting and transporting corn stover over the large distances required to supply a commercial-sized ethanol facility.biofuels, corn acreage, crop prices, ethanol production, food prices, Resource /Energy Economics and Policy,