a preliminary inquiry towards understanding physical and sensory related properties

... Molecular Size Distribution in Long-aged Food Beverages and Alcoholic Drinks: A Preliminary Inquiry towards Understanding Physical- and Sensory- Related Properties Pasquale Massimiliano Falcone and Paolo ... (comparable means and standard deviations) for all meat quality characteristics The validation data were within the range of calibration data for fat and calories For cholesterol and MC, a few ... cooked and split patty, and averaged to obtain a representative reading for each patty Therefore, each radiance spectra representing a patty was an average of 100 readings The simultaneous radiance...

Ngày tải lên: 02/04/2014, 15:05

... Justify your claim Verify the following claim If V and W are contravariant (or covariant) vector fields on M, and if is a real number, then V+W and ồV are again contravariant (or covariant) vector ... for every pair of tangent vector fields V and W, and every scalar (In the language of linear algebra, this says that F is a linear transformation.) Proposition 4.7 (Covariant Fields are One-Form ... vector has local and ambient coordinates equal to each other, and equal to dxi = ồi, dt which are the same as the original coordinates In other words, the tangent vectors are the same as ordinary...

Ngày tải lên: 17/03/2014, 14:28

... a differentiable map,” Scientiae Mathematicae Japonicae, vol 55, no 1, pp 17–24, 2002 [12] T Miura, S.-M Jung, and S.-E Takahasi, “Hyers-Ulam-Rassias stability of the Banach space valued linear ... Journal of Mathematical Analysis and Applications, vol 320, no 2, pp 549–561, 2006 [19] S.-M Jung, “Legendre’s differential equation and its Hyers-Ulam stability,” to appear in Abstract and Applied ... G Isac, and Th M Rassias, Stability of Functional Equations in Several Variables, Birkh¨ user, Boston, Mass, USA, 1998 a [5] D H Hyers and Th M Rassias, “Approximate homomorphisms,” Aequationes...

Ngày tải lên: 22/06/2014, 11:20

... Justify your claim Verify the following claim If V and W are contravariant (or covariant) vector fields on M, and if å is a real number, then V+W and åV are again contravariant (or covariant) vector ... correspond to linear transformations in linear algebra (2) We add and scalar multiply tensor fields in a manner similar to the way we these things to vector fields For instant, if A and B are type (1,2) ... is a function “-,-‘ that associates to each pair of smooth contravariant vector fields X and Y a scalar (field) “X, Y‘, satisfying the following properties Symmetry: “X, Y‘ = “Y, X‘ for all X and...

Ngày tải lên: 12/08/2014, 16:20

... same reason as above) (a) says that we measure the world line C as representing a particle traveling with light speed, and (b) says that we measure ordinary length in the usual way This motivates ... Introduction to Relativity First a general comment: We said in the last section that, at any point p in a Riemannian manifold M, we can find a local chart at p with the property that the metric tensor ... is a scalar Proposition 6.5 (Paramaterization by Arc Length) Let C be a non-null path xi = xi(t) in M Fix a point t = a on this path, and define a new function s (arc length) by s(t) = L (a, t)...

Ngày tải lên: 12/08/2014, 16:20

... will call the transformation from one Lorentz frame to another a generalized Lorentz transformation An Example of a Lorentz Transformation We would like to give a simple example of such a transformation ... are rotated—no longer parallel to the original axes) Now some reading to find the transformation for a pure boost in an arbitrary direction Covariant Differentiation Intuitively, by a parallel ... Exercise Set What can be said about the scalar ||dxi/dt||2 in a Lorentz frame for a particle traveling at (a) sub-light speed (b) super-light speed (a) Show that, if xi(t) is a timelike path in the...

Ngày tải lên: 12/08/2014, 16:20

... inertial) frames x and x– have the same parity if det D— > An orientation of M is an atlas of M such that all the charts have the same parity M is called orientable if it has such an atlas, and ... at each point We now show that it is a tensor If x– and y– are any two oriented coordinate systems at m and change-of-coordinate matrices D and E with respect to some inertial frame x at m, and ... throw a ball in the air, then the path is curved and also a geodesic Does this mean that our earthly coordinates are not inertial? Answer Yes At each instant in time, we can construct a local inertial...

Ngày tải lên: 12/08/2014, 16:20

... V(2) and V(3) as the spatial basis vectors Using parallel translation, we obtain a similar set of vectors at each point along the path (The fact that the curve is a geodesic guarantees that parallel ... facts (a) Restricting your attention to Riemannian 4-manifolds, let A, B, and C be vectors at m, and suppose—as you may—that you have chosen an inertial frame at m with the property 1 that A ... gkl), deduce that the scalar | |A B…C||2 is numerically equal to square of the volume of the parallelepiped spanned by the vectors a, b and c (Note also that | |A B…C||2, being a scalar, does not...

Ngày tải lên: 12/08/2014, 16:20

... in half by scaling all linear dimensions down by a factor å, then the areas scale down by a factor of å , whereas the volume (and hence mass) scales down by a factor å3 In other words, T (å 2a ) ... properties A1 -A3 listed below A1 Locally, M is Minkowski spacetime (so that special relativity holds locally) This means that, if we diagonalize the scalar product on the tangent space at any point, ... form ∆V) However, every covariant vector Y* defines a 3-volume as follows Recall that a one-form at a point p is a linear real-valued function on the tangent space Tp at that point If it is non-zero,...

Ngày tải lên: 12/08/2014, 16:20

... combination of gab,ij, gab,i and gab, and must also be symmetric (since T is) Examples of such a tensors are the Ricci tensors Rab, gabR, as well as gab Let us take a linear combination as our candidate: ... original law A = R was wrong 103 Gravity and Antigravity Newton's law of gravity says that a particle of mass M exerts a force on another particle of mass m according to the formula F =- r GMmr ... candidate: Rab + µgabR + ¡gab = kTab (II) We now apply the conservation laws Tab|b = 0, giving (Rab + µgabR)|b = (a) since gab|b = already (Exercise Set #4) But in §9 we also saw that (Rab - gabR)|b...

Ngày tải lên: 12/08/2014, 16:20

... is unable to hold up against the gravitational forces, and the star collapses (see the next section) overwhelming even the quantum mechanical forces In fact, it collapses to a singularity, a point ... that a particle fired away from the black hole will move (initially at least) so as to increase r, then your argument proves that r increases no matter what direction the particle is fired Back ... show that this is equivalent to saying that l i m ∞(r) = l i m ¡(r) = Hence obtain the formula r→+Ï r→+Ï 2M e2∞ = r A Derivation of Newton's Law of Gravity (a) Show that, at a large distance R...

Ngày tải lên: 12/08/2014, 16:20

... 127 and protons combine to form neutrons (and neutrinos which are nearly massless and noninteracting) A sufficiently dense star is unstable against such an interaction and all electrons and protons ... One can think of the star as a gas of positive charge atomic nuclei and negative charge electrons Each metal nucleus is a few thousand times heavier than the set of electrons that were attached ... bigger than earth -a reasonable estimate for a white 125 dwarf star! The mass density ® may also be calculated assuming the radius R0: ® ‡ 109 kg/m3 = 105 ¿ density of steel On the average, the...

Ngày tải lên: 12/08/2014, 16:20

... mole at 298 K for a particular state, a particular allotrope, particular molecular complexity, a particular molar mass, and a particular degree of dissolution Tro, Chemistry: A Molecular Approach ... Relative Standard Entropies States • the gas state has a larger entropy than the liquid state at a particular temperature • the liquid state has a larger entropy than the solid state at a particular ... the particles result in the same macrostate Tro, Chemistry: A Molecular Approach 17 Macrostates and Probability There is only one possible arrangement that gives State A and one that gives State...

Ngày tải lên: 28/11/2013, 01:12

... it as a startup tank and a running tank The key to running a diesel on straight vegetable oil is to heat the vegetable oil at every stage—in the fuel tank, fuel hose, and fuel filter The vegetable ... to Use Vegetable Oil as a Fuel Diesel engines that are found in cars, trucks, generators, boats, buses, trains, planes, pumping stations, tractors, and agricultural equipment can all run on fuel ... this batch is unsuccessful, make another batch and increase the amount of lye to 0.65 grams If that batch is unsuccessful, make another batch with 0.75 grams of lye Make sure you can make biodiesel...

Ngày tải lên: 27/01/2014, 14:20

... policies, and behavioral change.3 Speakers, panelists, and other workshop participants discussed examples of each, along with advantages, drawbacks, and related issues In some cases, there was broad agreement; ... Many Details Remain Unresolved Participants generally agreed that a cap -and- trade approach, while imperfect, seems more politically feasible than a carbon tax Although a carbon tax might be a ... emitting GHGs can fluctuate with the permit market A detailed discussion of the advantages and disadvantages of a cap -and- trade policy as opposed to a carbon tax can be found in Chapter Two Regardless...

Ngày tải lên: 06/03/2014, 21:20

... Warsaw, Banacha 2, 02-097 Warszawa Poland witeks@hydra.mimuw.edu.pl Marco Sammartino Department of Mathematics, Via Archirafi 34, 90123 Palermo Italy marco@math.unipa.it Vincenzo Sciacca Department ... with applications to algebra and analysis II, Z CHATZIDAKIS, D MACPHERSON, A PILLAY & A WILKIE (eds) Finite von Neumann algebras and masas, A. M SINCLAIR & R.R SMITH Number theory and polynomials, ... the fact that each of these reactions take place at different rates and blood is maintained in a delicate state of balance while a myriad of biochemical reactions take place On the other hand if...

Ngày tải lên: 14/03/2014, 10:20

... ensemble averages of internuclear distances and angles from the reactant to the product states are listed in Table The internuclear distances and angles based on the ensemble average of atomic Cartesian ... Wong and J Gao Table Selected ensemble-average internuclear distances and bond angles at the reactant, transition, intermediate, and product states in the active site of PDE These ve states are ... Characterization of a catalytic ligand bridging metal ions in phosphodiesterases and by molecular dynamics simulations and hybrid quantum mechanical molecular mechanical calculations Biophys J...

Ngày tải lên: 14/03/2014, 23:20

... talk given at the Conference on Mathematics, Mechanics, and Informatics, Hanoi, 7/10/2006, on the occasion of 50th Anniversary of Department of Mathematics, Mechanics and Informatics, Vietnam ... [9], H.Inaba), A : D (A) ⊂ E → E and operator f : R+ × E → E is continuous in t and satisfies all conditions (5), (6), (7) And now, we introduce the delay differential equation: d p(t) = Ap(t) + ... Equations, Springer-Verlag, New York, Berlin, London, Paris, Tokyo, Hong kong, Barcelona, Heidelberg, Milan, Singapore, 2000 [11] A Pazy, Semigoup of linear operators and applications to partial...

Ngày tải lên: 22/03/2014, 11:20

... know,’ said Alice, and why it is you hate—C and D,’ she added in a whisper, half afraid that it would be offended again ‘Mine is a long and a sad tale!’ said the Mouse, turning to Alice, and sighing ... cats and dogs.’ It was high time to go, for the pool was getting quite crowded with the birds and animals that had fallen into it: there were a Duck and a Dodo, a Lory and an Eaglet, and several ... certainly: Alice turned and came back again ‘Keep your temper,’ said the Caterpillar ‘Is that all?’ said Alice, swallowing down her anger as well as she could ‘No,’ said the Caterpillar Alice...

Ngày tải lên: 24/03/2014, 00:20

... Justify your claim Verify the following claim If V and W are contravariant (or covariant) vector fields on M, and if is a real number, then V+W and ồV are again contravariant (or covariant) vector ... Hanno Rund TABLE OF CONTENTS Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions Smooth Manifolds and Scalar Fields Tangent Vectors and the Tangent Space Contravariant ... real-valued map : UE1 If U M, we sometimes call such a scalar field local If is a scalar field on M and x is a chart, then we can express as a smooth function of n the associated parameters...

Ngày tải lên: 27/03/2014, 11:52