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The energy transition towards a decarbonized economy requires focused and ambitious policies that must be taken through the agreement of governments, stakeholders, and private companies. The intermittency of renewable energy sources (RES) makes it necessary to implement energy storage systems (ESS) that allow for an uninterrupted supply of low-carbon power. Energy generation and consumption activities are responsible for 75% of global CO2 emissions. Particularly, energy use in commercial and residential buildings is the third major contributor after industry and agricultural activities. In this context, the SUDOE ENERGY PUSH project proposes an innovative pilot plant combining RES and hydrogen technologies for social housing decarbonization and self-sufficiency. The preliminary simulations results in savings up to 7,000 kWh per year of primary energy from the grid, 1,000 kg per year of CO2 emissions while consuming 100% clean electricity and more than 600 € per year in electricity bills

International audience; Flavin coenzymes are universally found in biological redox reactions. DNA photolyases, with their flavin chromophore (FAD), utilize blue light for DNA repair and photoreduction. The latter process involves two single-electron transfers to FAD with an intermittent protonation step to prime the enzyme active for DNA repair. Here we use time-resolved serial femtosecond X-ray crystallography to describe how light-driven electron transfers trigger subsequent nanosecond-to-microsecond entanglement between FAD and its Asn/Arg-Asp redox sensor triad. We found that this key feature within the photolyase-cryptochrome family regulates FAD re-hybridization and protonation. After first electron transfer, the FAD•- isoalloxazine ring twists strongly when the arginine closes in to stabilize the negative charge. Subsequent breakage of the arginine-aspartate salt bridge allows proton transfer from arginine to FAD•-. Our molecular videos demonstrate how the protein environment of redox cofactors organizes multiple electron/proton transfer events in an ordered fashion, which could be applicable to other redox systems such as photosynthesis.

For a complex Banach space X with open unit ball $$B_X,$$ consider the Banach algebras $$\mathcal {H}^\infty (B_X)$$ of bounded scalar-valued holomorphic functions and the subalgebra $$\mathcal {A}_u(B_X)$$ of uniformly continuous functions on $$B_X.$$ Denoting either algebra by $$\mathcal {A},$$ we study the Gleason parts of the set of scalar-valued homomorphisms $$\mathcal {M}(\mathcal {A})$$ on $$\mathcal {A}.$$ Following remarks on the general situation, we focus on the case $$X = c_0,$$ giving a complete characterization of the Gleason parts of $$\mathcal {M}(\mathcal {A}_u(B_{c_0}))$$ and, among other things, showing that every fiber in $$\mathcal {M}(\mathcal {H}^\infty (B_{c_0}))$$ over a point in $$B_{\ell _\infty }$$ contains $$2^c$$ discs lying in different Gleason parts.

It was reported in 1995 that T7 and Taq DNA polymerases possess 3′-esterase activity, but without follow-up studies. Here we report that the 3′-esterase activity is intrinsic to the Thermococcus sp. 9°N DNA polymerase, and that it can be developed into a continuous method for DNA sequencing with dNTP analogs carrying a 3′-ester with a fluorophore. We first show that 3′-esterified dNTP can be incorporated into a template-primer DNA, and solve the crystal structures of the reaction intermediates and products. Then we show that the reaction can occur continuously, modulated by active site residues Tyr409 and Asp542. Finally, we use 5′-FAM-labeled primer and esterified dNTP with a dye to show that the reaction can proceed to ca. 450 base pairs, and that the intermediates of many individual steps can be identified. The results demonstrate the feasibility of a 3′-editing based DNA sequencing method that could find practical applications after further optimization., Shiuan-Woei LinWu et al. presents a DNA sequencing technology with high accuracy, using 9°N DNA polymerase. This study expands the current portfolio of enzymes equipped with 3′-esterase activity and shows the feasibility of a 3′-editing-based DNA sequencing.

In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.

The authors would like to thank Bill Johnson for kindly answering several inquiries., We study the Bishop–Phelps–Bollobás property for numerical radius restricted to the case of compact operators (BPBp-nu for compact operators in short). We show that C0(L) spaces have the BPBp-nu for compact operators for every Hausdorff topological locally compact space L. To this end, on the one hand, we provide some techniques allowing to pass the BPBp-nu for compact operators from subspaces to the whole space and, on the other hand, we prove some strong approximation property of C0(L) spaces and their duals. Besides, we also show that real Hilbert spaces and isometric preduals of ℓ1 have the BPBp-nu for compact operators.

A new estimate for the Bohr radius of the family of holomorphic functions in the n-dimensional polydisk is provided. This estimate, obtained via a new approach, is sharper than those that are known up to date.

We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series $${\mathcal {H}}^\infty ({\mathbb {C}}_+^2)$$ . We also show how the composition operators of this space of Dirichlet series are related to the composition operators of the corresponding spaces of holomorphic functions. Finally, we give a characterization of the superposition operators in $${\mathcal {H}}^\infty ({\mathbb {C}}_+)$$ and in the spaces $${\mathcal {H}}^p$$ .

Vibrio cholerae is the causative agent of the diarrheal disease cholera, for which biofilm communities are considered to be environmental reservoirs. In endemic regions, and after algal blooms, which may result from phosphate enrichment following agricultural runoff, the bacterium is released from biofilms resulting in seasonal disease outbreaks. However, the molecular mechanism by which V. cholerae senses its environment and switches lifestyles from the biofilm‐bound state to the planktonic state is largely unknown. Here, we report that the major biofilm scaffolding protein RbmA undergoes autocatalytic proteolysis via a phosphate‐dependent induced proximity activation mechanism. Furthermore, we show that RbmA mutants that are defective in autoproteolysis cause V. cholerae biofilms to grow larger and mechanically stronger, correlating well with the observation that RbmA stability directly affects microbial community homeostasis and rheological properties. In conclusion, our biophysical study characterizes a novel phosphate‐dependent breakdown pathway of RbmA, while microbiological data suggest a new, sensory role of this biofilm scaffolding element.

We introduce and investigate the mth polarization constant of a Banach space X for the numerical radius. We first show the difference between this constant and the original mth polarization constant associated with the norm by proving that the new constant is minimal if and only if X is strictly convex, and that there exists a Banach space which does not have an almost isometric copy of $$\ell _1^2$$ , such that the second polarization constant for the numerical radius is maximal. We also give a negative answer for complex Banach spaces to the question of Choi and Kim (J Lond Math Soc (2) 54(1):135–147, 1996) whether $$\frac{\sum _{k=1}^m k^m ~\left( {\begin{array}{c}m\\ k\end{array}}\right) }{m!}$$ is the optimal upper bound for the mth polarization constant for arbitrary $$m\in \mathbb {N}$$ . Finally, we generalize the result of Garcia et al. (Proc Am Math Soc 142(4):1229–1235, 2014) that, for 2-homogeneous polynomials, the numerical index of a complex lush space is greater or equal than 1/3.

This study was implemented to assess the Sessile Bioindicators in Permanent Quadrats (SBPQ) underwater environmental alert method. The SBPQ is a non-invasive and low-cost protocol; it uses sessile target species (indicators) to detect environmental alterations (natural or anthropic) at either the local or global (i.e., climate change) scale and the intrusion of invasive species. The SBPQ focuses on the monitoring of preselected sessile and sensitive benthic species associated with rocky coralligenous habitats using permanent quadrats in underwater sentinel stations. The selected target species have been well documented as bioindicators that disappear in the absence of environmental stability. However, whether these species are good indicators of stability or, in contrast, suffer variations in long-term coverage has not been verified. The purpose of this study was to assess the part of the method based on the hypothesis that, over a long temporal series in a highly structured and biodiverse coralligenous assemblage, the cover of sensitive sessile species does not change over time if the environmental stability characterising the habitat is not altered. Over a ten-year period (2005-2014), the sublittoral sessile biota in the Straits of Gibraltar Natural Park on the southern Iberian Peninsula was monitored at a 28 m-deep underwater sentinel stations. Analyses of the coverages of target indicator species (i.e., Paramuricea clavata and Astroides calycularis) together with other accompanying sessile organisms based on the periodic superimposition of gridded images from horizontal and vertical rocky surfaces allowed us to assess the effectiveness of the method. We conclude that no alterations occurred during the study period; only minimal fluctuations in cover were detected, and the method is reliable for detecting biological changes in ecosystems found in other geographical areas containing the chosen indicator species at similar dominance levels.

We study the group invariant continuous polynomials on a Banach space $X$ that separate a given set $K$ in $X$ and a point $z$ outside $K$. We show that if $X$ is a real Banach space, $G$ is a compact group of $\mathcal{L} (X)$, $K$ is a $G$-invariant set in $X$, and $z$ is a point outside $K$ that can be separated from $K$ by a continuous polynomial $Q$, then $z$ can also be separated from $K$ by a $G$-invariant continuous polynomial $P$. It turns out that this result does not hold when $X$ is a complex Banach space, so we present some additional conditions to get analogous results for the complex case. We also obtain separation theorems under the assumption that $X$ has a Schauder basis which give applications to several classical groups. In this case, we obtain characterizations of points which can be separated by a group invariant polynomial from the closed unit ball., Comment: 17 pages

In the study of the spectra of algebras of holomorphic functions on a Banach space E, the bidual E″ has a central role, and the spectrum is often shown to be locally homeomorphic to E″. In this paper we consider the problem of spectra of subalgebras invariant under the action of a group (functions f such that f ○ g = f). It is natural to attempt a characterization in terms of the space of orbits E″/~ obtained from E″ through the action of the group, so we pursue this approach here and introduce an analytic structure on the spectrum in some situations. In other situations we encounter some obstacles: in some cases, the lack of structure of E″/~ itself; in others, problems of weak continuity and non-approximability of functions in the algebra. We also define a convolution operation related to the spectrum.

We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically isomorphic between themselves. In a precise way, let { λ n } be a strictly increasing sequence of positive real numbers such that lim n → ∞ ⁡ λ n = ∞ . We denote by H ∞ ( λ n ) the complex normed space of all Dirichlet series D ( s ) = ∑ n b n λ n − s , which are convergent and bounded on the half plane [ Re s > 0 ] , endowed with the norm ‖ D ‖ ∞ = sup Re s > 0 ⁡ | D ( s ) | . If (⁎) there exists q > 0 such that inf n ⁡ ( λ n + 1 q − λ n q ) > 0 , then H ∞ ( λ n ) is a Banach space. Further, if there exists a strictly increasing sequence { r n } of positive numbers such that the sequence { log ⁡ r n } is Q -linearly independent, μ n = r α for n = p α , and { λ n } is the increasing rearrangement of the sequence { μ n } , then H ∞ ( λ n ) is isometrically isomorphic to H ∞ ( B c 0 ) . With this condition (⁎) we explain more explicitly the optimal cases of the difference among the abscissas σ c , σ b , σ u and σ a .

Cyclobutane pyrimidine dimer (CPD) photolyases harness the energy of blue light to repair UV-induced DNA CPDs. Upon binding, CPD photolyases cause the photodamage to flip out of the duplex DNA and into the catalytic site of the enzyme. This process, called base-flipping, induces a kink in the DNA, as well as an unpaired bubble, which are stabilized by a network of protein–nucleic acid interactions. Previously, several co-crystal structures have been reported in which the binding mode of CPD photolyases has been studied in detail. However, in all cases the internucleoside linkage of the photodamage site was a chemically synthesized formacetal analogue and not the natural phosphodiester. Here, the first crystal structure and conformational analysis via molecular-dynamics simulations of a class II CPD photolyase in complex with photodamaged DNA that contains a natural cyclobutane pyrimidine dimer with an intra-lesion phosphodiester linkage are presented. It is concluded that a highly conserved bubble-intruding region (BIR) mediates stabilization of the open form of CPD DNA when complexed with class II CPD photolyases.

Photolyases and cryptochromes form an almost ubiquitous family of blue light photoreceptors involved in the repair and maintenance of DNA integrity or regulatory control. We found that one cryptochrome from the green alga Chlamydomonas reinhardtii (CraCRY) is capable of both, control of transcript levels and the sexual cycle of the alga in a positive (germination) and negative manner (mating ability), as well as catalyzing the repair of UV-DNA lesions. Its 1.6 Å crystal structure shows besides the FAD chromophore an aromatic tetrad that is indispensable in animal-like type I cryptochromes for light-driven change of their signaling-active redox state and formation of a stable radical pair. Given CraCRY’s catalytic activity as (6-4) photolyase in vivo and in vitro, we present the first co-crystal structure of a cryptochrome with duplex DNA comprising a (6-4) pyrimidine–pyrimidone lesion. This 2.9 Å structure reveals a distinct conformation for the catalytic histidine His1, H357, that challenges previous models of a single-photon driven (6-4) photolyase mechanism.

Giving a partial answer to a conjecture formulated by Aron, Boyd, Ryan and Zalduendo, we show that if a real Banach space X is not linearly and continuously injected into a Hilbert space, t...

Given a proper holomorphic mapping $$g:\varOmega \subseteq {\mathbb {C}}^{n}\longrightarrow \varOmega ' \subseteq {\mathbb {C}}^{n}$$ and an algebra of holomorphic functions $${\mathcal {B}}$$ (e.g. $${\mathscr {P}}(K)$$ where $$K\subset \varOmega $$ is a compact set, $${\mathcal {H}}(U)$$ , A(U) or $${\mathcal {H}}^{\infty }(U)$$ where U is an open and bounded set with $$\overline{U}\subset \varOmega $$ ), we study the subalgebra $${\mathcal {B}}_{g}$$ of all functions compatible with the equivalence relation defined by the proper mapping g. We provide alternative representations of these algebras and describe the fibers in their spectra. Among other examples we relate the algebras of functions that are invariant under permutations and the algebras of functions defined on the symmetrized polydisk.

We study the Bishop-Phelps-Bollobàs property (BPBp) for compact operators. We present some abstract techniques that allow us to carry the BPBp for compact operators from sequence spaces to function spaces. As main applications, we prove the following results. Let X and Y be Banach spaces. If (c0, Y) has the BPBp for compact operators, then so do (C0(L), Y) for every locally compactHausdorò topological space L and (X, Y) whenever X* is isometrically isomorphic to . If X* has the Radon-Nikodým property and (X), Y) has the BPBp for compact operators, then so does (L1(μ, X), Y) for every positive measure μ; as a consequence, (L1(μ, X), Y) has the BPBp for compact operators when X and Y are finite-dimensional or Y is a Hilbert space and X = c0 or X = Lp(v) for any positive measure v and 1 < p < ∞. For , if (X, (Y)) has the BPBp for compact operators, then so does (X, Lp(μ, Y)) for every positive measure μ such that L1(μ) is infinite-dimensional. If (X, Y) has the BPBp for compact operators, then so do (X, L∞(μ, Y)) for every σ-finite positive measure μ and (X, C(K, Y)) for every compact Hausdorff topological space K.

We study the Bishop–Phelps–Bollobas property and the Bishop–Phelps–Bollobas property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair ( l 1 ( X ) , Y ) to have the BPBp for bilinear forms and prove that on L 1 ( μ ) the numerical radius and the norm of a multilinear mapping are the same. We also show that L 1 ( μ ) fails the BPBp-nu for multilinear mappings although L 1 ( μ ) satisfies it in the operator case for every measure μ.

We study the existence of separation theorems by polynomials that are invariant under a group action. We show that if G is a finite subgroup of \(\textit{GL}(n,{\mathbb {C}})\), K is a set in \({\mathbb {C}}^{n}\) that is invariant under the action of G and z is a point in \({\mathbb {C}}^{n}\setminus K\) that can be separated from K by a polynomial Q, then z can be separated from K by a G-invariant polynomial P. Furthermore, if Q is homogeneous then P can be chosen to be homogeneous. As a particular case, if K is a symmetric polynomially convex compact set in \({\mathbb {C}}^{n}\) and \(z\notin K\) then there exists a symmetric polynomial that separates z and K.

We study the existence of infinite-dimensional vector spaces in the sets of norm-attaining operators, multilinear forms, and polynomials. Our main result is that, for every set of permutations $P$ of the set $\{1,\ldots,n\}$ , there exists a closed infinite-dimensional Banach subspace of the space of $n$ -linear forms on $\ell_{1}$ such that, for all nonzero elements $B$ of such a subspace, the Arens extension associated to the permutation $\sigma$ of $B$ is norm-attaining if and only if $\sigma$ is an element of $P$ . We also study the structure of the set of norm-attaining $n$ -linear forms on $c_{0}$ .

We exhibit a new class of Banach spaces Y such that the pair ( c 0 , Y ) has the Bishop–Phelps–Bollobas property for operators. This class contains uniformly convex Banach spaces and spaces with the property β of Lindenstrauss. We also provide new examples of spaces in this class.

A classical result of Fatou gives that every bounded holomorphic function on the disc has radial limits for almost every point in the torus, and the limit function belongs to the Hardy space H_\infty of the torus. This property is no longer true when we consider vector-valued functions. The Banach spaces X for which this property is satisfied are said to have the analytic Radon-Nikodym property (ARNP). Some important equivalent reformulations of ARNP are studied in this chapter. Among others, X has ARNP if and only if each X-valued H_p- function f on the disc has radial limits almost everywhere on the torus (and not only H_\infty-functions). Even more, in this case each such f has non-tangential limits within any Stolz region. The basic tools are subharmonic functions and certain maximal inequalities. Finally, it is shown that if X has the ARNP, then every L_p of functions taking values in X with a finite measure also has ARNP.