Downloads & Free Reading Options - Results

We show that if you represent all primes with less than n-digits as points in n-dimensional space, then they can be stored and retrieved conveniently using n-dimensional geometry. Also once you have calculated all the prime numbers less than n digits, it is very easy to find out if a given number having less than n-digits is or is not a prime. We do this by separating all the primes which are represented by points in n-dimension space by planes. It so turns out that the number of planes q, required to separate all the points represented by primes less than n-digit, are very few in number. Thus we obtain a very efficient storage and retrieval system in n-dimensional space. In addition the storage and retieval repository has the property that when new primes are added there is no need to start all over, we can begin where we last left off and add the new primes in the repository and add new planes that separate them as and when necessary. Also we can arrange matters such that the repository can begin to accept larger primes which has more digits say n' where n' > n. The algorithm does not make use of any property of prime numbers or of integers in general,except for the fact that any n-digit integer can be represented as a point in n-dimension space. Therefore the method can serve to be a storage and retrieval repository of any set of given integers, in practical cases they can represent information. Thus the algorithm can be used to devise a very efficient storage and retrieval system for large amounts of digital data.

Explicit formulas are obtained for a family of continuous mappings of p-adic numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space \~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for which the Cantor set and the Sierpinski triangle are images of the unit balls in $\Qn{2}$ and $\Qn{3}$. In each of the families, the subset of the embeddings is found. For these embeddings, the Hausdorff dimensions are calculated and it is shown that the fractal measure on the image of $\Qp$ coincides with the Haar measure on $\Qp$. It is proved that under certain conditions, the image of the $p$-adic solenoid is an invariant set of fractional dimension for a dynamic system. Computer drawings of some fractal images are presented.

Explicit formulas are obtained for a family of continuous mappings of p-adic numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space \~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for which the Cantor set and the Sierpinski triangle are images of the unit balls in $\Qn{2}$ and $\Qn{3}$. In each of the families, the subset of the embeddings is found. For these embeddings, the Hausdorff dimensions are calculated and it is shown that the fractal measure on the image of $\Qp$ coincides with the Haar measure on $\Qp$. It is proved that under certain conditions, the image of the $p$-adic solenoid is an invariant set of fractional dimension for a dynamic system. Computer drawings of some fractal images are presented.

Explicit formulas are obtained for a family of continuous mappings of p-adic numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space \~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for which the Cantor set and the Sierpinski triangle are images of the unit balls in $\Qn{2}$ and $\Qn{3}$. In each of the families, the subset of the embeddings is found. For these embeddings, the Hausdorff dimensions are calculated and it is shown that the fractal measure on the image of $\Qp$ coincides with the Haar measure on $\Qp$. It is proved that under certain conditions, the image of the $p$-adic solenoid is an invariant set of fractional dimension for a dynamic system. Computer drawings of some fractal images are presented.

Explicit formulas are obtained for a family of continuous mappings of p-adic numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space \~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for which the Cantor set and the Sierpinski triangle are images of the unit balls in $\Qn{2}$ and $\Qn{3}$. In each of the families, the subset of the embeddings is found. For these embeddings, the Hausdorff dimensions are calculated and it is shown that the fractal measure on the image of $\Qp$ coincides with the Haar measure on $\Qp$. It is proved that under certain conditions, the image of the $p$-adic solenoid is an invariant set of fractional dimension for a dynamic system. Computer drawings of some fractal images are presented.

Parametric geometry of numbers is a new theory, recently created by Schmidt and Summerer, which unifies and simplifies many aspects of classical Diophantine approximations, providing a handle on problems which previously seemed out of reach. Our goal is to transpose this theory to fields of rational functions in one variable and to analyze in that context the problem of simultaneous approximation to exponential functions.

In this paper, we give a new, short, simple and geometric proof of the optimal er-godization time for linear flows on tori. This result was first obtained by Bourgain, Golse and Wennberg in [BGW98] using Fourier analysis. Our proof uses geometry of numbers: it follows trivially from a Diophantine duality that was established by the author and Fischler in [BF13].

In this paper, we give a new, short, simple and geometric proof of the optimal er-godization time for linear flows on tori. This result was first obtained by Bourgain, Golse and Wennberg in [BGW98] using Fourier analysis. Our proof uses geometry of numbers: it follows trivially from a Diophantine duality that was established by the author and Fischler in [BF13].

In this paper, we give a new, short, simple and geometric proof of the optimal er-godization time for linear flows on tori. This result was first obtained by Bourgain, Golse and Wennberg in [BGW98] using Fourier analysis. Our proof uses geometry of numbers: it follows trivially from a Diophantine duality that was established by the author and Fischler in [BF13].

In this paper, we give a new, short, simple and geometric proof of the optimal er-godization time for linear flows on tori. This result was first obtained by Bourgain, Golse and Wennberg in [BGW98] using Fourier analysis. Our proof uses geometry of numbers: it follows trivially from a Diophantine duality that was established by the author and Fischler in [BF13].

Double Hurwitz numbers count branched covers of the projective line with fixed branch points, with simple branching required over all but two points 0 and infinity, and the branching over 0 and infinity specified by partitions of the degree (with m and n parts respectively). Single Hurwitz numbers have a rich structure, explored by authors in many fields. The ELSV formula relates single Hurwitz numbers to intersection theory on the moduli space of curves, and has led to many consequences. We determine the structure of double Hurwitz numbers using geometry, algebra, and representation theory. Our motivation is geometric: we give strong evidence that double Hurwitz numbers are top intersections on a universal Picard variety. In particular, we prove a piecewise-polynomiality result analogous to that implied by the ELSV formula. In the case m=1 and n is arbitrary, we conjecture an ELSV-type formula, and show it to be true in genus 0 and 1. The corresponding Witten-type correlation function has a better structure than that for single Hurwitz numbers, and it satisfies many geometric properties, such as the string and dilaton equations, and a genus expansion ansatz analogous to that of Itzykson and Zuber. We give a symmetric function description of the double Hurwitz generating series, which leads to explicit formulae for double Hurwitz numbers with given m and n. In the case where m is fixed but not necessarily 1, we prove a topological recursion on the corresponding generating series, which leads to closed-form expressions for double Hurwitz numbers and an analogue of the Goulden-Jackson polynomiality conjecture (an early conjectural variant of the ELSV formula).

Air inlet for turbojet engines having variable angle two-dimensional compression surface and fixed-geometry subsonic diffuser

Given $n$ independent random marked $d$-vectors (points) $X_i$ distributed with a common density, define the measure $\nu_n=\sum_i\xi_i$, where $\xi_i$ is a measure (not necessarily a point measure) which stabilizes; this means that $\xi_i$ is determined by the (suitably rescaled) set of points near $X_i$. For bounded test functions $f$ on $R^d$, we give weak and strong laws of large numbers for $\nu_n(f)$. The general results are applied to demonstrate that an unknown set $A$ in $d$-space can be consistently estimated, given data on which of the points $X_i$ lie in $A$, by the corresponding union of Voronoi cells, answering a question raised by Khmaladze and Toronjadze. Further applications are given concerning the Gamma statistic for estimating the variance in nonparametric regression.

We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techniques to determine, for any base global field $F$ of characteristic not 2, the density of discriminants of field extensions of degree at most 5 over $F$.

The Kullback-Leibler information number is a well-known measure of statistical distance between probability distributions. Previous authors have shown that when endowed with this distance measure, the space of probability distributions possesses geometrical properties analogous to Euclidean geometry. This paper proves a new geometrical property by showing that one can in fact define the shortest line between two probability distributions as well as its mid-point. It turns out that the probability distributions comprising this line have long ago been used as a tool in the important problem of testing statistical hypotheses involving nuisance parameters. Apart from pure mathematical convenience, there has been little justification for its use. The results in this paper are the first attempt at such explanation.

A variable-geometry annular cascade-type inlet is proposed and demonstrated. Such an inlet yielded total-pressure recoveries of 0.84 and 0.53 at Mach numbers of 1.9 and 3.05., respectively. Unity mass-flow ratios were obtained at each Mach number with only marginal subcritical stability ranges of mass-flow ratio (?0.03). Angles of attack up to 6 percent produced only moderate decreases in performance.

A variable-geometry annular cascade-type inlet is proposed and demonstrated. Such an inlet yielded total-pressure recoveries of 0.84 and 0.53 at Mach numbers of 1.9 and 3.05., respectively. Unity mass-flow ratios were obtained at each Mach number with only marginal subcritical stability ranges of mass-flow ratio (?0.03). Angles of attack up to 6 percent produced only moderate decreases in performance.

327 p. 24 cm

327 p. 24 cm

In-flight F-111 data on total and static pressure from left inlet during automatically scheduled and manually controlled off-schedule positioning of spike at Mach 0.68 to 2.18

In-flight F-111 data on total and static pressure from left inlet during automatically scheduled and manually controlled off-schedule positioning of spike at Mach 0.68 to 2.18

Analyses of surface pressure data from wind tunnel tests conducted in the Propulsion Wind Tunnel (16T) on the 0.1- and 0.2-scale models of the YF-17 aircraft and flight tests conducted at the NASA Dryden Flight Research Center with the prototype YF-17 were conducted to substantiate the effectiveness of the subscale wind tunnel test techniques currently used at AEDC to provide data to evaluate throttle-dependent effects. The data were obtained at Mach numbers 0.6, 0.9, and 1.2 at characteristic Reynold numbers based on fuselage length from 14 million to 250 million. The data obtained at Mach numbers 0.6 and 0.9 indicate that valid techniques are available to obtain subscale wind tunnel data that are directly applicable to aft-end throttle-dependent flight performance prediction. The wind tunnel plume simulation techniques, however, do not provide data for directly predicting the flight vehicle, aft-end, calculated loads at Mach number 1.2. Additional corrections must be applied to the data to compensate for temperature effects associated with afterburning operations, such as that encountered at Mach 1.2.

Analyses of surface pressure data from wind tunnel tests conducted in the Propulsion Wind Tunnel (16T) on the 0.1- and 0.2-scale models of the YF-17 aircraft and flight tests conducted at the NASA Dryden Flight Research Center with the prototype YF-17 were conducted to substantiate the effectiveness of the subscale wind tunnel test techniques currently used at AEDC to provide data to evaluate throttle-dependent effects. The data were obtained at Mach numbers 0.6, 0.9, and 1.2 at characteristic Reynold numbers based on fuselage length from 14 million to 250 million. The data obtained at Mach numbers 0.6 and 0.9 indicate that valid techniques are available to obtain subscale wind tunnel data that are directly applicable to aft-end throttle-dependent flight performance prediction. The wind tunnel plume simulation techniques, however, do not provide data for directly predicting the flight vehicle, aft-end, calculated loads at Mach number 1.2. Additional corrections must be applied to the data to compensate for temperature effects associated with afterburning operations, such as that encountered at Mach 1.2.

Analyses of surface pressure data from wind tunnel tests conducted in the Propulsion Wind Tunnel (16T) on the 0.1- and 0.2-scale models of the YF-17 aircraft and flight tests conducted at the NASA Dryden Flight Research Center with the prototype YF-17 were conducted to substantiate the effectiveness of the subscale wind tunnel test techniques currently used at AEDC to provide data to evaluate throttle-dependent effects. The data were obtained at Mach numbers 0.6, 0.9, and 1.2 at characteristic Reynold numbers based on fuselage length from 14 million to 250 million. The data obtained at Mach numbers 0.6 and 0.9 indicate that valid techniques are available to obtain subscale wind tunnel data that are directly applicable to aft-end throttle-dependent flight performance prediction. The wind tunnel plume simulation techniques, however, do not provide data for directly predicting the flight vehicle, aft-end, calculated loads at Mach number 1.2. Additional corrections must be applied to the data to compensate for temperature effects associated with afterburning operations, such as that encountered at Mach 1.2.

We study a lattice point counting problem for a class of families of domains in a Euclidean space. This class consists of anisotropically expanding bounded domains, which remain unchanged along some fixed linear subspace and expand in directions, orthogonal to this subspace. We find the leading term in the asymptotics of the number of lattice points in such family of domains and prove remainder estimates in this asymptotics under various conditions on the lattice and the family of domains. As a consequence, we prove an asymptotic formula for the eigenvalue distribution function of the Laplace operator on a flat torus in adiabatic limit determined by a linear foliation with a nontrivial remainder estimate.

We define and investigate extension groups in the context of Arakelov geometry. The 'arithmetic extension groups' we introduce are extensions by groups of analytic types of the usual extension groups attached to $\O_X$-modules over an arithmetic scheme $X$. In this paper, we focus on the first arithmetic extension group - the elements of which may be described in terms of admissible short exact sequences of hermitian vector bundles over $X$ - and we especially consider the case when $X$ is an 'arithmetic curve', namely the spectrum $\Spec \O_K$ of the ring of integers in some number field $K$. Then the study of arithmetic extensions over $X$ is related to old and new problems concerning lattices and the geometry of numbers.

This paper concerns the \textbf{abstract geometry of numbers}: namely the pursuit of certain aspects of geometry of numbers over a suitable class of normed domains. (The standard geometry of numbers is then viewed as geometry of numbers over Z endowed with its standard absolute value.) In this work we study normed domains of "linear type", in which an analogue of Minkowski's linear forms theorem holds. We show that S-integer rings in number fields and coordinate rings of (nice) affine algebraic curves over an arbitrary ground field are of linear type. The theory is applied to quadratic forms in two ways, yielding a Nullstellensatz and a Small Multiple Theorem.

In this paper we develop some of the ideas belonging to W.Schmidt and L.Summerer to define intermediate Diophantine exponents and split Dyson's transference inequality into a chain of inequalities for intermediate exponents. This splitting generalizes the analogous result of M.Laurent and Y.Bugeaud for Khintchine's transference inequalities.

An experimental investigation was conducted in the AEDC 16-foot Transonic Wind Tunnel (16T) to determine both Reynolds number and nozzle afterbody configuration effects on model forebody and afterbody drag. The model was a sting-mounted body of revolution with interchangeable contoured, cylindrical, and 15-deg boattail configurations. Pressure and force data were obtained at Mach numbers from 0.60 to 1.40 and at unit Reynolds numbers from 1, 470,000 per foot to 5,300,000 per foot. The experimental results showed that large variations in afterbody drag levels produced no significant change in forebody drag. The data also revealed that all three configurations exhibited little or no Reynolds number dependence subsonically and that only the 15-deg boattail afterbody was affected by Reynolds number supersonically. It was also demonstrated that data precision and wind tunnel calibration can have a significant effect on model drag and should be given careful consideration.

An experimental investigation was conducted in the AEDC 16-foot Transonic Wind Tunnel (16T) to determine both Reynolds number and nozzle afterbody configuration effects on model forebody and afterbody drag. The model was a sting-mounted body of revolution with interchangeable contoured, cylindrical, and 15-deg boattail configurations. Pressure and force data were obtained at Mach numbers from 0.60 to 1.40 and at unit Reynolds numbers from 1, 470,000 per foot to 5,300,000 per foot. The experimental results showed that large variations in afterbody drag levels produced no significant change in forebody drag. The data also revealed that all three configurations exhibited little or no Reynolds number dependence subsonically and that only the 15-deg boattail afterbody was affected by Reynolds number supersonically. It was also demonstrated that data precision and wind tunnel calibration can have a significant effect on model drag and should be given careful consideration.

xix, 276 p. incl. front. 20 cm

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is a sequel to our previous paper arXiv:1105.1554, where we defined two types of intermediate Diophantine exponents, connected them to Schmidt exponents and split Dyson's transference inequality into a chain of inequalities for intermediate exponents. Here we present splitting of some other transference inequalities involving both regular and uniform Diophantine exponents.

Recently, W. M. Schmidt and L. Summerer introduced a new theory which allowed them to recover the main known inequalities relating the usual exponents of Diophantine approximation to a point in $\mathbb{R}^n$, and to discover new ones. They first note that these exponents can be computed in terms of the successive minima of a parametric family of convex bodies attached to the given point. Then they prove that the $n$-tuple of these successive minima can in turn be approximated up to bounded difference by a function from a certain class. In this paper, we show that the same is true within a smaller and simpler class of functions which we call rigid systems. We also show that conversely, given a rigid system, there exists a point in $\mathbb{R}^n$ whose associated family of convex bodies has successive minima which approximate that rigid system up to bounded difference. As a consequence, the problem of describing the joint spectrum of a family of exponents of Diophantine approximation is reduced to combinatorial analysis.

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one usually assumes that $V=T_g$ for some representation $T_g$ of a compact group $G$ on the C*-elliptic complex. We try to refuse this restriction in the present paper. The price to pay for this is twofold: (i) $ $ We have to define Lefschetz numbers valued in some larger group as $K_0(A)\o\C$. (ii) We have to deal with W*-algebras instead of general unital C*-algebras. To obtain these results we have got a number of by-product facts on the theory of Hilbert W*- and C*-modules and on bounded module operators on them which are of independent interest.

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one usually assumes that $V=T_g$ for some representation $T_g$ of a compact group $G$ on the C*-elliptic complex. We try to refuse this restriction in the present paper. The price to pay for this is twofold: (i) $ $ We have to define Lefschetz numbers valued in some larger group as $K_0(A)\o\C$. (ii) We have to deal with W*-algebras instead of general unital C*-algebras. To obtain these results we have got a number of by-product facts on the theory of Hilbert W*- and C*-modules and on bounded module operators on them which are of independent interest.

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one usually assumes that $V=T_g$ for some representation $T_g$ of a compact group $G$ on the C*-elliptic complex. We try to refuse this restriction in the present paper. The price to pay for this is twofold: (i) $ $ We have to define Lefschetz numbers valued in some larger group as $K_0(A)\o\C$. (ii) We have to deal with W*-algebras instead of general unital C*-algebras. To obtain these results we have got a number of by-product facts on the theory of Hilbert W*- and C*-modules and on bounded module operators on them which are of independent interest.

A lattice Delaunay polytope P is called perfect if its Delaunay sphere is the only ellipsoid circumscribed about P. We present a new algorithm for finding perfect Delaunay polytopes. Our method overcomes the major shortcomings of the previously used method. We have implemented and used our algorithm for finding perfect Delaunay polytopes in dimensions 6, 7, 8. Our findings lead to a new conjecture that sheds light on the structure of lattice Delaunay tilings.

We develop a global cohomology theory for number fields by offering topological cohomology groups, an arithmetical duality, a Riemann-Roch type theorem, and two types of vanishing theorem. As applications, we study moduli spaces of semi-stable lattices, and introduce non-abelian zeta functions for number fields.

The motivic nearby fiber is an invariant obtained from degenerating a complex variety over a disc. It specializes to the Euler characteristic of the original variety but also contains information on the variation of Hodge structure associated to the degeneration which is encoded as a limit mixed Hodge structure. However, this invariant is difficult to compute in practice. Using the techniques of tropical geometry we present a new formula for the motivic nearby fiber. Moreover, since there is a range of available software implementing the main algorithms in tropical geometry, our formula can be computed in practice. We specialize to the case of families of sch\"{o}n complex hypersurfaces of tori where we provide explicit formulas describing the action of the unipotent part of monodromy on the graded pieces (with respect to the Deligne weight filtration) of the cohomology with compact supports. These families are described combinatorially by a polyhedral subdivision of the associated Newton polytope. We develop new mixed Hodge theory-inspired combinatorial invariants of such subdivisions, among them the `refined limit mixed $h^*$-polynomial'. These invariants are related to Stanley's combinatorial study of subdivisions: in a companion combinatorial paper whose results are applied here, we situate our invariants in Stanley's theory where they become multi-variable extensions of his invariants. Our results generalize work of Danilov and Khovanski{\u\i} and Batyrev and Borisov on the Hodge numbers of hypersurfaces. We also present analogous formulas describing the action of the unipotent part of monodromy on the intersection cohomology groups of a family of sch\"on hypersurfaces of a projective toric variety.

This is a revised compilation of the papers arXiv:1105.1554 and arXiv:1105.5823. We develop some of the ideas belonging to W.Schmidt and L.Summerer to define intermediate Diophantine exponents and split several transference inequalities into a chain of inequalities for intermediate exponents.

This is a revised compilation of the papers arXiv:1105.1554 and arXiv:1105.5823. We develop some of the ideas belonging to W.Schmidt and L.Summerer to define intermediate Diophantine exponents and split several transference inequalities into a chain of inequalities for intermediate exponents.

Aerodynamic stability and drag coefficients were obtained for five configurations of a 0.166-scale tow target at Mach numbers from 0.5 to 0.90. The primary configuration variables were tip fin size and fin cant angle. Effects of a blunted ogive nose as compared to an inlet shape nose were also investigated.

Control of variable-geometry inlets at constant mach numbers with blunt lip diffuser

For this investigation, a seven-blade cascade of NACA 65-A506 airfoils with two inch chord, aspect ration of one, and solidity of 1.5 was used. This cascade used porous side wall suction to establish two-dimensional flow conditions. Flow Unit Reynolds numbers exceeding 2.5 million foot, and average free stream turbulence levels of 1% and 7% were used. Cascade geometry was varied in a manner similar to that used in current variable stator designs: maintaining axial direction and blade spacing constant, while varying incidence angle, stagger angle, and angle of attack. Incidence angles of -3, 0, and +3 deg. were investigated. Total pressure loss coefficient decreases through the cascade and may increase in the wake as incidence angle or free stream turbulence increase. The change in loss coefficient with increasing incidence was determined to be insignificant when compared with the change as a result of increased free stream turbulence. Blade suction surface pressure coefficients decrease sharply along the first 30% chord as incidence increases. The suction surface pressure coefficients show a uniform increase across the blade center span with additional free stream turbulence. Increases in incidence and free stream turbulence result in thicker boundary layers and suggest both earlier transition and intermittent separation on the forward half of the blade. Evidence also suggests that the location of the minimum loss incidence angle may change with additional free stream turbulence. Keywords: Compressor blades; Pressure distribution, Cascades fluid dynamics; Cascade structures; Boundary layer, Theses.

Wind-tunnel tests were conducted to investigate the side forces and yawing moments that can occur at high angles of attack and zero sideslip for cylindrical bodies of revolution. Two bodies having several tangent ogive forebodies with fineness ratios of 0.5, 1.5, 2.5, and 3.5 were tested. The forebodies with fineness ratios of 2.5 and 3.5 had several bluntnesses. The cylindrical afterbodies had fineness ratios of 7 and 13. The model components - tip, forebody, and afterbody - were tested in various rotational positions about their axes of symmetry. Most of the tests were conducted at a Mach number of 0.25, a Reynolds number of 0.32 x 10 to the 6th power, and with the afterbody that had a fineness ratio of 7 and with selected forebodies. The effect of Mach number was determined with the afterbody that had a fineness ratio of 13 and with selected forebodies at mach numbers from 0.25 to 2 at Reynolds number = 0.32 X 10 to the 6th power. Maximum angle of attack was 58 deg.

A fixed-geometry diffuser system was tested in an arc-heated, hypersonic, open-jet wind tunnel facility at Mach numbers between 14 and 18 and Reynolds numbers (based on nozzle exit diameter) between 8,900 and 25,000. Tests were conducted both with an empty test section and with conical models in the flow. Test variables included test section open-jet length, diffuser second-throat length, and diffuser inlet geometry. Diffuser efficiency improved with increased diffuser second-throat length, with increasing Reynolds number, and with the addition of conical models into the flow. Changes in open-jet length and diffuser inlet geometry had no appreciable effect on diffuser efficiency with an empty test section. A streamlined model support strut produced marked improvement in diffuser efficiency over a blunt support strut.

A fixed-geometry second-throat diffuser system was tested in an open- jet wind tunnel at Mach numbers 3.6 and 7.0. These tests were conducted at Reynolds numbers of 1,000,000 and 200,000, based on expansion nozzle exit diameter. The investigation was conducted to provide diffuser design criteria for the AEDC proposed Hypersonic True Temperature Tunnel (Tripltee). At M infinity = 3.6, empty test section diffuser efficiencies of 96% of normal shock recovery were achieved. Under similar conditions at M infinity = 7.0, efficiencies of 90% were obtained, thus establishing that reasonable diffuser efficiencies can be obtained at both Mach numbers with a single diffuser system. Tunnel operation was possible with conical models of up to 18-% blockage, but diffuser efficiency was reduced by 8 to 12%. Tunnel flow could not be established with models in the test section. Models of 8- to 10-% blockage would not permit establishment of tunnel flow at either M infinity = 3.6 or 7.0. It was necessary to inject the models into the flow after the tunnel was started. Limited diffuser heating rate data was obtained at M infinity = 7.0.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

With the help of the recently introduced parametric geometry of numbers by W. M. Schmidt and L. Summerer, we prove a strong version of a conjecture of Schmidt concerning the successive minima of a lattice.