For a finite abelian p-group A and a subgroup $\Gamma \le \operatorname {\mathrm {Aut}}(A)$ , we say that the pair $(\Gamma ,A)$ is fusion realizable if there is a saturated fusion system ${\mathcal {F}}$ over a finite p-group $S\ge A$ such that $C_S(A)=A$ , $\operatorname {\mathrm {Aut}}_{{\mathcal {F}}}(A)=\Gamma $ as subgroups of $\operatorname {\mathrm {Aut}}(A)$ , and . In this paper, we develop tools to show that certain representations are not fusion realizable in this sense. For example, we show, for $p=2$ or $3$ and $\Gamma $ one of the Mathieu groups, that the only ${\mathbb {F}}_p\Gamma $ -modules that are fusion realizable (up to extensions by trivial modules) are the Todd modules and in some cases their duals.

We show that Miller partition forcing preserves selective independent families and P-points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$ . In addition, we show that Shelah’s poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$ .

The interaction of intense, ultrashort laser pulses with ordered nanostructure arrays offers a path to the efficient creation of ultra-high-energy density (UHED) matter and the generation of high-energy particles with compact lasers. Irradiation of deuterated nanowires arrays results in a near-solid density environment with extremely high temperatures and large electromagnetic fields in which deuterons are accelerated to multi-megaelectronvolt energies, resulting in deuterium–deuterium (D–D) fusion. Here we focus on the method of fabrication and the characteristics of ordered arrays of deuterated polyethylene nanowires. The irradiation of these array targets with femtosecond pulses of relativistic intensity and joule-level energy creates a micro-scale fusion environment that produced $2\times {10}^6$ neutrons per joule, an increase of about 500 times with respect to flat solid CD2 targets irradiated with the same laser pulses. Irradiation with 8 J laser pulses was measured to generate up to 1.2 × 107 D–D fusion neutrons per shot.

In this paper we propose a new theory and methodology to tackle the problem of unifying Monte Carlo samples from distributed densities into a single Monte Carlo draw from the target density. This surprisingly challenging problem arises in many settings (for instance, expert elicitation, multiview learning, distributed ‘big data’ problems, etc.), but to date the framework and methodology proposed in this paper (Monte Carlo fusion) is the first general approach which avoids any form of approximation error in obtaining the unified inference. In this paper we focus on the key theoretical underpinnings of this new methodology, and simple (direct) Monte Carlo interpretations of the theory. There is considerable scope to tailor the theory introduced in this paper to particular application settings (such as the big data setting), construct efficient parallelised schemes, understand the approximation and computational efficiencies of other such unification paradigms, and explore new theoretical and methodological directions.

We finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian p-groups with an abelian subgroup of index p. In particular, this gives many new examples illustrating the enormous variety of exotic examples that can arise. In addition, we classify all simple fusion systems over infinite nonabelian discrete p-toral groups with an abelian subgroup of index p. In all of these cases (finite or infinite), we reduce the problem to one of listing all 𝔽pG-modules (for G finite) satisfying certain conditions: a problem which was solved in the earlier paper [15] using the classification of finite simple groups.

Light sheet fluorescence microscopy (LSFM) allows for high-resolution three-dimensional imaging with minimal photo-damage. By viewing the sample from different directions, different regions of large specimens can be imaged optimally. Moreover, owing to their good spatial resolution and high signal-to-noise ratio, LSFM data are well suited for image deconvolution. Here we present the Huygens Fusion and Deconvolution Wizard, a unique integrated solution for restoring LSFM images, and show that improvements in signal and resolution of 1.5 times and higher are feasible.

Development of a detonation wave due to α heating following short pulse laser irradiation in pre-compressed deuterium–tritium (DT) plasma is considered. The laser parameters required for development of a detonation wave are calculated. We find that a laser irradiance and energy of IL = 1.75 × 1023 W/cm2 and 12.8 kJ accordingly during 1.0 ps in a pre-compressed target at 900 g/cm3 creates an α heating fusion detonation wave. In this case, the nuclear fusion ignition conditions for the pre-compressed DT plasma are achieved along the detonation wave orbit.

A criterion for a two temperature plasma nuclear fusion ignition is derived by using a common model. In particular, deuterium-tritium (DT) and proton–boron11 (pB11) are considered for pre-compressed plasma. The ignition criterion is described by a surface in the three-dimensional space defined by the electron and ion temperatures Te, Ti, and the plasma density times the hot spot dimension, ρ·R. The appropriate fusion ion temperatures Ti are larger than 10 keV for DT and 150 keV for pB11. The required value of ρ·R for pB11 ignition is larger by a factor of 50 or more than for DT, depending on the electron temperature. Furthermore, our ignition criterion obtained here for pB11 fusion is practically impossible for equal electron and ion temperatures. In this paper it is suggested to use a two temperature laser induced shock wave in the intermediate domain between relativistic and non-relativistic shock waves. The laser parameters required for fast ignition are calculated. In particular, we find that for DT case one needs a 3 kJ/1 ps laser to ignite a pre-compressed target at about 600 g/cm3. For pB11 ignition it is necessary to use more than three orders of magnitude of laser energy for the same laser pulse duration.

Vertebral deformity and fusion are reported in four Pampus species, Pampus cinereus, Pampus echinogaster, Pampus liuorum and Pampus punctatissimus (family: Stromateidae) collected from Guangdong, China and from the Kii Peninsula, Honshu Island, Japan. All abnormalities were found in the caudal region of the vertebral column of the four specimens of Pampus examined, which included cases of missing vertebrae, lordosis and deformed centra. In addition, minor anomalies were also noticed in the abnormal specimen of Pampus liuorum. Possible causes such as genetic and epigenetic factors may be implicated in this anomaly.

A very efficient analytical method using an automated fusion machine as sample preparation tool and a wavelength-dispersive X-ray fluorescence (WDXRF) spectrometer for the determination of all the elements of interest for the iron ore industry has been optimized from the ISO 9516-1 standard method. This updated method allows for the simplification of both laboratory and spectrometry processes and so, in comparison with the original International Organization for Standardization (ISO) method, becomes less restrictive in practice. This method was used to prepare a large variety of iron ores and exploration samples from all over the world. Results of the prevailing XRF application based on pure oxide standards as described in the ISO standard method are compared to the results of a unique XRF calibration application based on certified reference materials (CRMs) for iron ores and iron ores exploration materials. The universal sample preparation fusion method for iron ores and exploration samples developed during the first phase of this project was used to select and evaluate a set of CRMs. Selected throughout the world from well-recognized sources, the chosen set of CRMs allows a wide coverage for all the elements of interest of the iron ore industry, excluding tin oxide. This fusion method allows a matrix match for materials from different origins. A critical evaluation of precision and accuracy has been performed against the ISO standard method. Reference materials not included in the calibration (control samples) was also investigated for accuracy evaluation. Furthermore, comparisons will be made between the data collected from this fusion method implemented in combination with a Bruker S4 Explorer WDXRF Spectrometer, and the analytical requirements of ISO. All deviations from the prevailing standard method parameters (calibration, standards, flux, Fluxer, etc.) will also be pointed out and discussed.