There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diﬀeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove ﬁrst that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...
The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982), and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging, computational geometry, visualization …).
Sums of two squares near perfect squares
by R. C. Vaughan∗∗∗ In memory of Pritish Limani (1983–2003) Abstract Let C be a nondegenerate planar curve and for a real, positive decreasing function ψ let C(ψ) denote the set of simultaneously ψ-approximable points lying on C. We show that C is of Khintchine type for divergence; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on C of C(ψ) is full. We also obtain the Hausdorﬀ measure analogue of the divergent Khintchine type result. ...
In this chapter you will learn: Structure of myoglobin and hemoglobin similar; understand oxygen binding curves (where high and low affinity binding occurs); understand positive cooperatively in relationship to oxygen binding to hemoglobin, be able to describe this in relationship to protein conformation and the sigmoidal oxygen binding curve; be able to describe T and R conformations of Hb; understand how oxygen binding changes Hb conformation; define allosteric interaction;...
The main goals of this chapter are to: Apply production possibilities analysis, increasing opportunity costs, and economic growth; explain how economic growth and international trade increase consumption possibilities; understand graphs, curves, and slopes as they relate to economics.
• A diode is a very useful non-linear device • It allows current to flow in one direction and prevents it flowing in the other
• When a positive voltage is applied across the diode then current will flow • The diode is said to be forward biased • When a negative voltage is applied then the diode is reverse biased and no current will flow
Diode Characteristic Curve
Forward Biased Diode
• A positive voltage is applied to circuit so current will flow • Diode effectively behaves like a short circuit when forward biased...
26.1 26.2 Introduction . Types of Bearings
Sliding Bearings • Rocker and Pin Bearings • Roller Bearings • Elastomeric Bearings • Curved Bearings • Pot Bearings • Disk Bearings
J. Muller International, Inc.
Selection of Bearings
Determination of Functional Requirements • Evaluation of Bearings • Preliminary Bearing Design
J. Muller International, Inc.
Design of Elastomeric Bearings
Design Procedure • Design Example
This paper describes the corrosion behaviour of the positive and negative electrodes of a lead–acid battery in 5 M H2SO4 with binary additives such as mixtures of phosphoric acid and boric acid, phosphoric acid and tin sulphate, and phosphoric acid and picric acid. The effect of these additives is examined from the Tafel polarisation curves, double layer capacitance and percentage of inhibition efﬁciency.
Calculating sensitivity and specificity requires selection of a decision value for the test to define the threshold value at or above which the test is considered "positive." For any given test, as this cut point is moved to improve sensitivity, specificity typically falls and vice versa.
This dynamic tradeoff between more accurate identification of subjects with disease versus those without disease is often displayed graphically as a receiver operating characteristic (ROC) curve (Fig. 3-1). An ROC curve plots sensitivity (y-axis) versus 1 – specificity (x-axis).
The ribbon itself forms an abstract letter ‘W’ (for World)
that changes colour from pink through blue into a green
that represents a green economy. The person’s position
in the ribbon is where the colour incidentally transitions
into green, signifying that people – you – are central to a
functional green economy and thus it must include you.
The light green part of the ribbon curves into a slight
horizon of the earth.
Web geometry is devoted to the study of families of foliations which are in general position. We restrict ourselves to the local situation, in the neighborhood of the origin in C2 , with d ≥ 1 complex analytic foliations of curves in general position. We are interested in the geometry of such conﬁgurations, that is, properties of planar d-webs which are invariant with respect to analytic local isomorphisms of C2 . The initiators of the subject are W. Blaschke, G. Thomsen and G. Bol in the 1930’s (cf. [B-B], [B] and for instance [H1]). ...
How and when such theoretical uncertainty will translate into actual market movements will
depend on market dynamics. Because of extreme monetary ease, short-term interest rates
have been close to zero for some time and markets expect policy rates to remain low. The
yield curve is quite steep yet long-term interest rates are very low by historical standards.
Graph 4 shows that the US dollar term spread has been around 250–350 basis points since
The transparency of the body beneath the drapery is a clear reference point to the
female reclining figures from the Parthenon pediment sculptures. This is obvious in
Albert Moore’s Beads (1875), which depicts two young women reclining asleep in
different positions on a soft fabric bench with their legs, breasts, nipples and small
folds of their stomachs clearly visible beneath their white diaphanous Greek clothes.
The response to target rate increases was positive and signiﬁcant at all maturities, but
smaller at the long end of the yield curve: a one percentage point increase in the Fed funds
target led to an increase of 55 basis points in the three-month T-bill rate, but only a 10
basis point increase in the 30-year bond yield. Recognizing that some Fed actions may
have been anticipated, Cook and Hahn also examined the relationship between changes in
interest rates and future changes in the target.
This article contributes to the general debate on the link between
population growth and the environment by analyzing the impact of
demographic factors on two air pollutants. At the same time, it also con-
tributes to a more focused debate on how population size and other
demographic factors should be taken into account in future projections of
air pollutant emissions.
Analytical expressions for the ratio of the root mean square fluctuation in atomic positions on the equilibrium lattice positions and the nearest neighbor distance and the mean melting curves of bcc binary alloys have been derived. This melting curve provides information on Lindemann’s melting temperatures of binary alloys with respect to any proportion of constituent elements and on their euctectic points. Numerical results for some bcc binary alloys are found to be in agreement with experiment. Keywords: Lindemann’s melting temperature, eutectic point, bcc binary alloys.
Health plans with Medicaid experience were positioned to respond more quickly than others
to language service requirements. Their knowledge of language services, derived from
responding to existing MediCal requirements and serving diverse populations, has provided
a foundation for new efforts. This is less likely to be the case with commercial-only plans
that face a steeper learning curve.
After completing this chapter, students will be able to: Relate why the demand curve of an oligopolist may be kinked, compare the incentives and obstacles to collusion among oligopolists, contrast the potential positive and negative effects of advertising, utilize additional game-theory terminology and applications.