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Yesterday Chainlink released price reference data for 25 of its decentralized oracle networks which, together, power more than $100m in DeFi. On this special interview episode, @nlw talks with Sergey Nazarov and Kain Warwick, the founders of Chainlink and Synthetix.

We start at the very basics. What are derivatives? What are they used for? Who uses them?

The history of derivatives from Ancient Greece to the Financial Crisis of 2007-2009.

In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality conditions for paraconcave functions. As applications, we use these second-order optimality conditions to study strict local minimizers of order two and provide sufficient and/or necessary conditions for ensuring the local minimizer. This work extends and generalizes the study on second-order optimality conditions from the finite-dimensional space to the Hilbert space.

Let $(X,d,p)$ be a pointed metric space. A pretangent space to $X$ at $p$ is a metric space consisting of some equivalence classes of convergent to $p$ sequences $(x_n), x_n \in X,$ whose degree of convergence is comparable with a given scaling sequence $(r_n), r_n\downarrow 0.$ A scaling sequence $(r_n)$ is normal if this sequence is eventually decreasing and there is $(x_n)$ such that $\mid d(x_n,p)-r_n\mid=o(r_n)$ for $n\to\infty.$ Let $\mathbf{\Omega_{p}^{X}(n)}$ be the set of pretangent spaces to $X$ at $p$ with normal scaling sequences. We prove that $\mathbf{\Omega_{p}^{X}(n)}$ is uniformly bounded if and only if $\{d(x,p): x\in X\}$ is a so-called completely strongly porous set. It is also proved that the uniform boundedness of $\mathbf{\Omega_{p}^{X}(n)}$ is an equivalent of the constancy of metric derivatives of all metrically differentiable mappings on $X$ in the open balls of a fixed radius centered at the marked points of pretangent spaces.

This article is from Journal of Insect Science , volume 6 . Abstract Experiments were conducted to study the bioefficacies of different plant/weed derivatives that affect the development of the pulse beetle, Callosobruchus maculates F. (Coleoptera: Bruchidae) fed on black gram, Vigna mungo, seeds. Plant extracts, powder, ash and oil from nishinda (Vitex negundo L.), eucalyptus (Eucalyptus globules Labill.), bankalmi (Ipomoea sepiaria K.), neem (Azadirachta indica L.), safflower (Carthamus tinctorius L.), sesame (Sesamum indicum L.) and bablah (Acacia arabica L.) were evaluated for their oviposition inhibition, surface protectant, residual toxicity and direct toxicity effects on C. maculates. The results showed that plant oils were effective in checking insect infestation. The least number of F1 adults emerged from black gram seeds treated with neem oil. The nishinda oil extract was the most toxic of three extracts tested (nishinda, eucalyptus and bankalmi). Bablah ash was the most effective compared to the powdered leaves of nishinda, eucalyptus and bankalmi. The powdered leaves and extracts of nishinda, eucalyptus and bankalmi, at a 3% mixture, provided good protection for black gram seeds by reducing insect oviposition, F1 adult emergence, and grain infestation rates. The oil treatment did not show adverse effects on germination capability of seeds, even after three months of treatment.

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Tim Kelly, founder and CEO of BitOoda joins the show. BitOoda is a firm that is innovating in the field of structured products based on Bitcoin hashrate and difficulty. We discuss:- Tim's background and the similarities he sees with cryptoassets vs. other asset classes- The mining ecosystem and how derivative contracts solve real business needs- The evolving market structure for derivatives and views on the regulatory landscapeTo learn more about BitOoda visit: http://bitooda.io/

Yesterday Chainlink released price reference data for 25 of its decentralized oracle networks which, together, power more than $100m in DeFi. On this special interview episode, @nlw talks with Sergey Nazarov and Kain Warwick, the founders of Chainlink and Synthetix respectively about: The evolution and goals of Synthetix, a novel type of derivatives exchange where users can interact with any asset with a price feed. The challenge Synthetix faced around spinning up their own oracles around price feedsThe history of their collaboration and how Synthetix came to work with ChainlinkChainlink approach to building decentralized oracles for data such as price feedsChainlink's announcement yesterday about the new published price reference data for 25 oracle networksThe state of the idea of decentralization, and how what was previously a concept is becoming operationalizedOne thing that gives them pause or scares them about DeFi and crypto and one thing that makes them excited for the future 

We extend the representations of finite-dimensional Lie algebra by derivations of the completed symmetric algebra of its dual to the derivations of a bigger algebra which includes the exterior algebra on the Lie algebra. This enables a construction of a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators between noncommutative differentials and coordinates are formal power series in partial derivatives. The square of the corresponding exterior derivative is zero like in the classical case, but the Leibniz rule is deformed.

This item represents an oral argument audio file as scraped from a U.S. Government website by Free Law Project.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

From pure liquid SO3 direct synthesis reactions were carried out with N2O5, NO2Cl, NOCl which yielded N2O54SO3, 3SO3, 2SO3-NO2Cl2SO3-NOCl2SO3 and NOCl2SO3, the latter being obtained for the first time in the pure state. In all cases the crystallized product was obtained by separating the constituents of the mixture and then going through a single viscous liquid phase.

Extreme calculus tutorial with 100 derivatives for your Calculus 1 class. You'll master all the derivatives and differentiation rules, including the power rule, product rule, quotient rule, chain rule, and more. We'll also cover implicit differentiation, logarithmic differentiation, and finding second derivatives. Plus, we'll dive into derivatives of all trigonometric and hyperbolic functions, as well as their inverses. Of course, we will also have the definition of the derivative.

Extreme calculus tutorial with 100 derivatives for your Calculus 1 class. You'll master all the derivatives and differentiation rules, including the power rule, product rule, quotient rule, chain rule, and more. We'll also cover implicit differentiation, logarithmic differentiation, and finding second derivatives. Plus, we'll dive into derivatives of all trigonometric and hyperbolic functions, as well as their inverses. Of course, we will also have the definition of the derivative.

Let $E_1,\dots ,E_k$ and $E$ be natural vector bundles defined over the category $\Cal Mf_m^+$ of smooth oriented $m$--dimensional manifolds and orientation preserving local diffeomorphisms, with $m\geq 2$. Let $M$ be an object of $\Cal Mf_m^+$ which is connected. We give a complete classification of all separately continuous $k$--linear operators $D\:\Ga _c(E_1M)\x\dots\x\Ga_c(E_kM)\to \Ga (EM)$ defined on sections with compact supports, which commute with Lie derivatives, i\.e\. which satisfy $$ \Cal L_X(D(s_1,\dots ,s_k))=\sum _{i=1}^kD(s_1,\dots ,\Cal L_Xs_i,\dots,s_k), $$ for all vector fields $X$ on $M$ and sections $s_j\in\Ga_c(E_jM)$, in terms of local natural operators and absolutely invariant sections. In special cases we do not need the continuity assumption. We also present several applications in concrete geometrical situations, in particular we give a completely algebraic characterization of some well known Lie brackets.

We propose improvements in numerical evaluation of symmetric stable density and its partial derivatives with respect to the parameters. They are useful for more reliable evaluation of maximum likelihood estimator and its standard error. Numerical values of the Fisher information matrix of symmetric stable distributions are also given. Our improvements consist of modification of the method of Nolan (1997) for the boundary cases, i.e., in the tail and mode of the densities and in the neighborhood of the Cauchy and the normal distributions.

I consider the thermodynamics of the BTZ black hole in the presence of the higher curvature and gravitational Chern-Simons terms, and its statistical entropy. I propose a new thermodynamical entropy, which being {\it non-negative} manifestly, such as the second law, as well as the first law, of thermodynamics is satisfied. I show that the new \therl entropy agrees perfectly with the statistical entropy for $all$ the values of the conformal factor of the higher curvature terms and the coupling constant of the gravitational Chern-Simons term, in contrast to some disagreements in the literatures. The agreement with both the higher curvature and gravitational Chern-Simons terms is possible because of an appropriate balancing of them, though it is not a trivial matter because of a conflict in the appropriate Hilbert space for a well-defined conformal field theory for each term.

In certain Lorentz-covariant higher-derivative field theories of spins < or =1, would-be ultraviolet divergences generate color-singlet poles as infrared divergences. Absence of higher-order poles implies ten-dimensional supersymmetric Yang-Mills with bound-state supergravity, in close analogy with open string theory.

The conductance G of a quantum dot with single-mode ballistic point contacts depends sensitively on external parameters X, such as gate voltage and magnetic field. We calculate the joint distribution of G and dG/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singularity at zero and algebraic tails. While G and dG/dX are correlated, the ratio of dG/dX and $\sqrt{G(1-G)}$ is independent of G. Coulomb interactions change the distribution of dG/dX, by inducing a transition from the grand-canonical to the canonical ensemble. All these predictions can be tested in semiconductor microstructures or microwave cavities.

In this paper we provide a complete list of spin-2 cubic interaction vertices with two derivatives. We work in (anti) de Sitter space with dimension d >= 4 and arbitrary value of cosmological constant and use simple metric formalism without any auxiliary or Stueckelberg fields. We separately consider cases with one, two and three different spin-2 fields entering the vertex where each field may be massive, massless or partially massless one. The connection of our results with massive (bi)gravity theories is also briefly discussed.

D. Leviatan has investigated the behavior of the higher order derivatives of approximation polynomials of the differentiable function $f$ on $[-1,1]$. Especially, when $P_n$ is the best approximation of $f$, he estimates the differences $\|f^{(k)}-P_n^{(k)}\|_{L_\infty([-1,1])}$, $k=0,1,2,...$. In this paper, we give the analogies for them with respect to the differentiable functions on $\mathbb{R}$, and we apply the result to the monotone approximation.

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane

This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fixed point via contraction mapping. This leads us to develop an accurate iterative numerical scheme for valuation. Specifically, we solve a sequence of linear inhomogeneous PDEs, whose solutions converge to the fixed point price function. We apply our methodology to compute the bid and ask prices for both defaultable equity and fixed-income derivatives, and illustrate the non-trivial effects of counterparty risk, collateralization ratio and liquidation convention on the bid-ask spreads.

The aim of the paper is twofold. First, we introduce analogs of (partial) derivatives on certain Noncommutative algebras, including some enveloping algebras and their "braided counterparts", namely, the so-called modified Reflection Equation algebras. By using these derivatives we construct an analog of the de Rham complex on these algebras. Second, we discuss deformation property of some quantum algebras and show that contrary to a commonly held view, in the so-called q-Witt algebra there is no analog of the PBW theorem. In this connection, we discuss different forms of the Jacobi condition related to quadratic-linear algebras.

Some properties of a Local discontinuous Galerkin (LDG) algorithm are demonstrated for the problem of evaluting a second derivative $g = f_{xx}$ for a given $f$. (This is a somewhat unusual problem, but it is useful for understanding the initial transient response of an algorithm for diffusion equations.) LDG uses an auxiliary variable to break this up into two first order equations and then applies techniques by analogy to DG algorithms for advection algorithms. This introduces an asymmetry into the solution that depends on the choice of upwind directions for these two first order equations. When using piecewise linear basis functions, this LDG solution $g_h$ is shown not to converge in an $L_2$ norm because the slopes in each cell diverge. However, when LDG is used in a time-dependent diffusion problem, this error in the second derivative term is transient and rapidly decays away, so that the overall error is bounded. I.e., the LDG approximation $f_h(x,t)$ for a diffusion equation $\partial f / \partial t = f_{xx}$ converges to the proper solution (as has been shown before), even though the initial rate of change $\partial f_h / \partial t$ does not converge. We also show results from the Recovery discontinuous Galerkin (RDG) approach, which gives symmetric solutions that can have higher rates of convergence for a stencil that couples the same number of cells.

We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reaching generalization of the explicit Brauer-Siegel theorem both for number fields and function fields.

We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reaching generalization of the explicit Brauer-Siegel theorem both for number fields and function fields.

Computational procedures are presented for evaluating the sensitivity derivatives of the vibration frequencies and eigenmodes of framed structures. Both a displacement and a mixed formulation are used. The two key elements of the computational procedure are: (a) Use of dynamic reduction techniques to substantially reduce the number of degrees of freedom; and (b) Application of iterative techniques to improve the accuracy of the derivatives of the eigenmodes. The two reduction techniques considered are the static condensation and a generalized dynamic reduction technique. Error norms are introduced to assess the accuracy of the eigenvalue and eigenvector derivatives obtained by the reduction techniques. The effectiveness of the methods presented is demonstrated by three numerical examples.

Computational procedures are presented for evaluating the sensitivity derivatives of the vibration frequencies and eigenmodes of framed structures. Both a displacement and a mixed formulation are used. The two key elements of the computational procedure are: (a) Use of dynamic reduction techniques to substantially reduce the number of degrees of freedom; and (b) Application of iterative techniques to improve the accuracy of the derivatives of the eigenmodes. The two reduction techniques considered are the static condensation and a generalized dynamic reduction technique. Error norms are introduced to assess the accuracy of the eigenvalue and eigenvector derivatives obtained by the reduction techniques. The effectiveness of the methods presented is demonstrated by three numerical examples.

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Dynamic stability derivatives of twin-jet fighter model for angles of attack from -10 deg to 110 deg

An order of magnitude study of the ratios of successive polynomial derivatives yields information about the number of roots at an approached root point and the approximate location of a root point from a nearby point. The location approximation improves as a root is approached, so a powerful convergence procedure becomes available. These principles are developed into a computer program which finds the roots of polynomials with real number coefficients.

Summarized are the aerodynamic center, alpha and q- aeroelastic effects on fighter-type aircraft in the 18,700 N gross range. The results indicate that with proper tailoring of planform (fixed or variable sweep), stiffner and elastic axis location it is possible to minimize trim requirements between selected extreme conditions. The inertial effects were found to be small for this class of aircraft.

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We study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model subspace $K_B$ generated by the Blaschke product $B$

We study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model subspace $K_B$ generated by the Blaschke product $B$

Background: Pyrans are one of the most significant skeletons of oxygen-containing heterocyclic molecules, which exhibit a broad spectrum of medicinal applications. Green one-pot methodologies for synthesizing these heterocyclic molecules have received significant attention. The paper focusses on a simple approach to synthesize 4H-pyran derivatives by one pot multi-component reaction of aromatic aldehyde , β-ketoester or β-diketone with the use of Nd 2 O 3 as recyclable and efficient catalyst . Methods: The reagents ethyl acetoacetate (2mmol) and 4-chlorobenzaldehyde (1mmol) and varying amount of L-proline or Nd 2 O 3 catalyst were stirred or refluxed in PEG-400, water or H 2 O/EtOH (1:1) solvent to yield 4H pyran. The reaction time and yield of the product was monitored. 20 mmol of Nd 2 O 3 catalyst was sufficient to catalyze the reaction in good yield. The optimized conditions of the reaction were effectively implemented to synthesise various 4H pyran derivatives. The synthesized compounds were characterized and confirmed by different spectroscopic techniques like 1 H NMR and FTIR. The values reported are well in agreement with the expected values. Results: The results yielded lesser reaction time of around 30 to 54 mins with a yield of around 82 to 94 %. The reaction required only 20mmol catalyst in (1:1, v/v, ml) of H 2 O/C 2 H 5 OH mixed solvents. It demonstrates the low cost, simple work up process using H 2 O/ C 2 H 5 OH as greener solvents. Conclusions: Neodymium (III) oxide (Nd 2 O 3 ) is a powdered rare earth metal oxide used as a novel catalyst which can be recovered through simple filtration, rinsed with hot ethanol, and dried at 150 0 C for further use. The recovered catalyst can be reused successfully at least three times with minimal loss in activity.

In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize time, we use a similar approach to the discrete partial derivative method, which is a structure-preserving method for the gradient flows of graphs. For the approximation of curves, we use B-spline curves. Owing to the smoothness of B-spline functions, we can directly address higher order derivatives. In the last part of the paper, we consider some numerical examples of the elastic flow, which exhibit topology-changing solutions and more complicated evolution. Videos illustrating our method are available on YouTube.

In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize time, we use a similar approach to the discrete partial derivative method, which is a structure-preserving method for the gradient flows of graphs. For the approximation of curves, we use B-spline curves. Owing to the smoothness of B-spline functions, we can directly address higher order derivatives. In the last part of the paper, we consider some numerical examples of the elastic flow, which exhibit topology-changing solutions and more complicated evolution. Videos illustrating our method are available on YouTube.

In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize time, we use a similar approach to the discrete partial derivative method, which is a structure-preserving method for the gradient flows of graphs. For the approximation of curves, we use B-spline curves. Owing to the smoothness of B-spline functions, we can directly address higher order derivatives. In the last part of the paper, we consider some numerical examples of the elastic flow, which exhibit topology-changing solutions and more complicated evolution. Videos illustrating our method are available on YouTube.

In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize time, we use a similar approach to the discrete partial derivative method, which is a structure-preserving method for the gradient flows of graphs. For the approximation of curves, we use B-spline curves. Owing to the smoothness of B-spline functions, we can directly address higher order derivatives. In the last part of the paper, we consider some numerical examples of the elastic flow, which exhibit topology-changing solutions and more complicated evolution. Videos illustrating our method are available on YouTube.

Fortune's Andy Serwer says that the financial instruments are at the core of the economic mess.

The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was demonstrated that the local Holder exponent/ dimension was directly related to the maximum order for which LFD existed. We have extended this definition to directional-LFD for functions of many variables and demonstrated its utility with the help of simple examples.