Motivic and $$\ell $$-adic realizations of the category of singularities of the zero locus of a global section of a vector bundle

We study the motivic and $$\ell $$ ℓ -adic realizations of the dg category of singularities of the zero locus of a global section of a line bundle over a regular scheme. We will then use the formula obtained in this way together with a theorem due to D. Orlov and J. Burke–M. Walker to give a formula for the $$\ell $$ ℓ -adic realization of the dg category of singularities of the zero locus of a global section of a vector bundle. In particular, we obtain a formula for the $$\ell $$ ℓ -adic realization of the dg category of singularities of the special fiber of a scheme over a regular local ring of dimension n.

Koszul complexes and spectral sequences associated with Lie algebroids

We study some spectral sequences associated with a locally free $${{\mathscr {O}}}_X$$ O X -module $${{\mathscr {A}}}$$ A which has a Lie algebroid structure. Here X is either a complex manifold or a regular scheme over an algebraically closed field k. One spectral sequence can be associated with $${{\mathscr {A}}}$$ A by choosing a global section V of $${{\mathscr {A}}}$$ A , and considering a Koszul complex with a differential given by inner product by V. This spectral sequence is shown to degenerate at the second page by using Deligne’s degeneracy criterion. Another spectral sequence we study arises when considering the Atiyah algebroid $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ D E of a holomolorphic vector bundle $${{\mathscr {E}}}$$ E on a complex manifold. If V is a differential operator on $${{\mathscr {E}}}$$ E with scalar symbol, i.e, a global section of $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ D E , we associate with the pair $$({{\mathscr {E}}},V)$$ ( E , V ) a twisted Koszul complex. The first spectral sequence associated with this complex is known to degenerate at the first page in the untwisted ($${{\mathscr {E}}}=0$$ E = 0 ) case.

Substitution Attacks against Message Authentication

This work introduces Algorithm Substitution Attacks (ASAs) on message authentication schemes. In light of revelations concerning mass surveillance, ASAs were initially introduced by Bellare, Paterson and Rogaway as a novel attack class against the confidentiality of encryption schemes. Such an attack replaces one or more of the regular scheme algorithms with a subverted version that aims to reveal information to an adversary (engaged in mass surveillance), while remaining undetected by users. While most prior work focused on subverting encryption systems, we study options to subvert symmetric message authentication protocols. In particular we provide powerful generic attacks that apply e.g. to HMAC or Carter–Wegman based schemes, inducing only a negligible implementation overhead. As subverted authentication can act as an enabler for subverted encryption (software updates can be manipulated to include replacements of encryption routines), we consider attacks of the new class highly impactful and dangerous.

Very Flat Optical Frequency Comb Generation based on Polarization Modulator and Recirculation Frequency Shifter

We propose and experimentally demonstrate a novel scheme to generate a flat and stable optical frequency comb by using recirculation frequency shifter (RFS) loop and polarization-modulator based single-side-band modulator (PSSBM). An ultra-flat 5-carriers generated by a polarization modulator is set as the seed light source of the recirculating loop, and the recirculation times is greatly reduced compared with the regular scheme based on RFS. Through theoretical analysis and experiment simulations, it is shown that the optical frequency comb of high quality with 50 spectral lines and the flatness fluctuation of less than 1 dB can be achieved.

Étale Fundamental Groups of Strongly $\boldsymbol{F}$-Regular Schemes

We prove that a strongly $F$-regular scheme $X$ admits a finite, generically Galois, and étale-in-codimension-one cover $\tilde X \to X$ such that the étale fundamental groups of $\tilde X$ and $\tilde X_{{\mathrm{reg}}}$ agree. Equivalently, every finite étale cover of $\tilde X_{{\mathrm{reg}}}$ extends to a finite étale cover of $\tilde X$. This is analogous to a result for complex klt varieties by Greb, Kebekus, and Peternell.

Testing for Jumps

This chapter is devoted to the most basic question about jumps: are they present at all? As seen in Chapter 5, this question can be answered unambiguously when the full path of the underlying process X is observed over the time interval of interest [0, T]. However, we suppose that X is discretely observed along a regular scheme with lag Δ‎₀, so no jump can actually be exactly observed, since observing a large discrete increment may be suggestive that a jump took place, but provides no certitude. We wish to derive testing procedures which are at least consistent. This can only be done under some structural hypotheses on X, and the property of being an Itô semimartingale is a suitable one.

Subcategories of singularity categories via tensor actions

We obtain, via the formalism of tensor actions, a complete classification of the localizing subcategories of the stable derived category of any affine scheme that has hypersurface singularities or is a complete intersection in a regular scheme; in particular, this classifies the thick subcategories of the singularity categories of such rings. The analogous result is also proved for certain locally complete intersection schemes. It is also shown that from each of these classifications one can deduce the (relative) telescope conjecture.

Effect of Training on Shipboard Oil Pollution Violations

Industrialization has brought forth comforts and catastrophes. In the regular scheme of technological developments, the worst malady faced by man is the defilement of the environment. Shipping, being a heavily regulated industry, has contributed less in comparison to other land-based polluters, but the enormity of an oil spill and the post-spill clean-ups are reasons enough for countries to tighten the pollution laws. Today, any action violating these laws is seen as a crime. Ships are being detained, penalized for pollution violations. Environmental concerns and criminalizing incidents have become issues of concern. While considering these viewpoints, a worthwhile approach would be to look at the seafarer training. Assessment of the competency of the shipboard officer is largely carried out by examinations and onboard assessments. This could be extended to other means such as research surveys. The chapter projects inputs from a study undertaken to assess the level of training and awareness in pollution matters amongst shipboard officers.

Design and Optimization FCCU Absorption-Stabilization System through Process Simulation

In this preparation, FCCU main fractionator and corresponding absorption-stabilization system are systemically simulated on the basis of industrial data. Through analysis, a heat exchanging column is added to improve the flowsheet before rich gas cooler to make good use of heat of the compressed rich gas. To decrease LPG lost along with dry gas, a dry gas compression-expansion refrigeration circle is proposed to offer refrigeration capacity in place of the cooling water for the absorber pumparounds. Compared with the regular scheme, energy consumption and C3+ components in dry gas is reduced respectively by 17.18% and 7.16% and LPG yield is increased by 0.41% simultaneously.

Extending families of curves over log regular schemes

In this paper, we generalize to the “log regular case” a result of de Jong and Oort which states that any morphism satisfying certain conditions from the complement of a divisor with normal crossings in a regular scheme to a moduli stack of stable curves extends over the entire regular scheme. The proof uses the theory of “regular log schemes” — i.e., schemes with singularities like those of toric varieties – due to K. Kato ([12]). We then use this extension theorem to prove that under certain natural conditions any scheme which is a successive fibration of smooth hyperbolic curves may be compactified to a successive fibration of stable curves.