# Haut PDF Distributed primality proving and the primality of (2 +1)/3

### Distributed primality proving and the primality of (2 +1)/3

17

### Proving the safety of highly-available distributed objects

**and**

**2**. for any state σ ∈ S, σ Inv. Corollary

**1**.

**The**soundness proposition (

**1**) is a direct consequence

**of**Lemma 5 ...to

**proving**invariants

**of**shared-memory ...

29

### Decomposability of graphs into subgraphs fulfilling the 1-2-3 Conjecture

**the**thesis ...),

**1**≤ dS(v) ≤ dH 0 (v) − 10 10 ...uv

**of**F 0 , one

**of**its ends must belong to V (H 0 ) – we then arbitrarily choose one edge from S incident with this end

**and**add ...

14

### Neighbour-Sum-2-Distinguishing Edge-Weightings: Doubling the 1-2-3 Conjecture

**the**bounds given in Section

**2**for many classes

**of**...improve

**the**bound in Corollary 2.2,

**and**this would surely require new dedicated ...classes

**of**graphs, let us mention ...

16

### Sulfone Based-Electrolytes for Lithium-Ion Batteries: Cycling Performances and Passivation Layer Quality of Graphite and LiNi 1/3 Mn 1/3 Co 1/3 O 2 Electrodes

**and**after 5 cycles

**of**charge-discharge performed in MESL + LiTFSI with or without FEC (5%) at room temperature

**and**40 °C ...Only

**the**principal peaks (C 1s, F 1s, S 2p) corresponding ...

10

### Prediction of a New Layered Polymorph of FeS 2 with Fe 3+ S 2– (S 2 ) 1/2 2- Structure

**and**mainly differ in how

**the**S

**2**

**2**- dimers are arranged around

**the**Fe

**2**+ c T c c - b

**1**f

**1**) 26

**1**

**1**) 26 for marcasite ...structures.

**The**...

22

### On a List Variant of the Multiplicative 1-2-3 Conjecture

**The**

**1**-

**2**-

**3**Conjecture asks whether almost all graphs can be (edge-)labelled with

**1**,

**2**,

**3**so that no two adjacent vertices are incident to

**the**same sum ...

24

### 1-2-3 Conjecture in Digraphs: More Results and Directions

**the**number

**of**vertices

**of**D. We focus on

**proving**

**the**general ...vertex

**of**D. According to

**the**induction hypothesis,

**the**digraph D 0 obtained by removing v from D ...

22

### Further Results on an Equitable 1-2-3 Conjecture

**of**

**the**number

**of**assigned

**2**’s, that is so huge that it cannot be caught up by

**the**labelling freedom

**of**G m

**and**

**the**copies

**of**

**the**corrector ...

28

### Proving the safety of highly-available distributed objects (Extended version)

**and**

**2**. for any state σ ∈ S, σ Inv. Corollary

**1**.

**The**soundness proposition (

**1**) is a direct consequence

**of**Lemma 5 ...to

**proving**invariants

**of**shared-memory ...

38

### Further Evidence Towards the Multiplicative 1-2-3 Conjecture

**1**-

**2**-

**3**Conjecture; multiset version; product version; 4-chromatic ...graphs.

**1**. Introduction This work takes place in

**the**general context

**of**distinguishing labellings, ...

16

### Explicit primality criteria for $h\cdot 2^n\pm 1$

**1**, where µ is a 16-th root

**of**unity such that µπ

**2**is a primary element in Z[ζ 16 ...].

**The**paper is organized as follows. In Section

**2**, we introduce

**the**high order power ...

21

### Proving Computational Geometry Algorithms in TLA+2

**and**N ext are defined in

**the**Graham’s algorithm specification.

**The**proofs

**of**formula ...lay

**the**emphasis on

**the**proof

**of**

**the**formula (IV.

**3**) which is ...

5

### The L^2 -Alexander torsion of 3-manifolds

**the**above both det N (G) (A)

**and**det N (G) (B) are at least one, it follows that det N (G) (A) = ...Q

**and**B a matrix over Z[G]. It follows immediately from

**the**aforementioned result ...

47

### Synthesis of 1,2-methano-tetrahydrofuran derivatives and 1´,2´-methano-2´,3´-dideoxynucleosides as potential antivirals

**and**acetonitrile (24 mL) at 0 °C, phosphoryl chloride ...period

**of**

**3**minutes using a syringe pump, followed by triethylamine ...mmol).

**The**heterogeneous mixture was stirred for ...

143

### Closed-form expressions of the eigen decomposition of 2 x 2 and 3 x 3 Hermitian matrices

**The**eigen decomposition

**of**covariance matrices is at

**the**core

**of**many data analysis tech- ...niques.

**The**study

**of**

**2**-components or

**3**-components vector ...

4

### The preparation of certified calibration solutions for azaspiracid-1, -2, and -3, potent marine biotoxins found in shellfish

**of**lipophilic polyether marine biotoxins that were first detected in harvested mussels (Mytilus edulis) from Killary Harbour on

**the**west coast

**of**Ireland in ...those

**of**diarrhetic ...

11

### A comparative study of the Ruddlesden-Popper series, Lan+1NinO3n+1 (n=1, 2 and 3), for solid-oxide fuel-cell cathode applications

**the**different values obtained for α when

**the**data is fitted over

**the**temperature ranges 348 K–548 K

**and**548– 1173 K, which are summarized in Table

**3**....

**The**change in α over ...

7

### New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH 2 ) 3 )(CH 3 NH 3 ) n Pb n I 3 n +1 : Structure, Properties, and Photovoltaic Performance

**the**US DOE Office

**of**...for

**the**National Nuclear Security Administration

**of**

**the**US DOE under contract ...at

**the**Institut des Sciences Chimiques de Rennes, which received ...

58

### Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances

**the**now well-documented

**1**:

**2**resonance relationship, where two eigenfrequencies (ω

**1**, ω

**2**) are such that ω

**2**2ω

**1**...nonlinearity,

**and**is now classical, since ...

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