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White Croc-Embossed London Mid-Top Sneakers Giuseppe Zanotti IN4ee2hX
White Croc-Embossed London Mid-Top Sneakers Giuseppe Zanotti

Before we describe our cryptosystem, we define the following notion which is one of our key ideas to construct our cryptosystem.

Definition 3.1.

Define a map \(\sigma : \mathbb {Z}^{n} \longrightarrow \mathbb {Z}\) by \(\underline {i} \mapsto \sum \underline {i}\) . A polynomial \(X \in \mathbb {Z}[\underline {x}]\) is if \(\sigma |_{\Lambda _{X}}\) is injective. In other words, is of if and only if for each \(k \in \mathbb {Z}\) , has at most one term of degree .

Remark 3.2.

We can prove that there is no general algorithm to solve an arbitrary diophantine equation of degree increasing type in \(\mathbb {Z}\) . This can be seen as follows: Suppose \(T \in \mathbb {Z}[\underline {x}]\) is an arbitrary polynomial. It is easy to see that by making a change of variables \(x_{i} \mapsto x_{i}^{q_{i}}\) with suitable ’s, we can make \(T\left (x_{1}^{q_{1}},\ldots,x_{n}^{q_{n}}\right)\) of degree increasing type. Thus if there exists an algorithm to solve an arbitrary diophantine equation of degree increasing type, then it can solve an arbitrary diophantine equation, which contradicts Matijasevič’s result [ 10 ].

Example 3.3.

If (,):=5 +12 +7 +6+5, then is of degree increasing type.

Let \(X \in \mathbb {Z}[\underline {x}]\) be a polynomial of degree increasing type. Then we can define a total order in Λ f as follows: for \(\underline {i}_{1}\) , \(\underline {i}_{2} \in \Lambda _{f}\) , we define \(\underline {i}_{1} \geq \underline {i}_{2}\) if \(\sum \underline {i}_{1} \geq \sum \underline {i}_{2}\) . Since Λ f is finite, there is a maximal element \(\underline {k}\) . We call the coefficient of degree \(\sum \underline {k}\) of X the leading coefficient of X and denote it by l d ( X ).

$$F_{i}(\underline{x}) := \tilde{m} + s_{i}f + r_{i}X (i = 1,2,3), $$

Now, we describe our cryptosystem.

Secret key

Choose a vector \(\underline {a} = (a_{1},\ldots,a_{n}) \in \mathbb {Z}^{n}\) of a suitable size such that \(\gcd (a_{i},d) =1\) for =1,…,. Make them secret.

Public key

Choose integers and of suitable sizes such that \(\gcd (e,\varphi (d)) =1\) . Choose an irreducible polynomial \(X(\underline {x}) \in \mathbb {Z}[\underline {x}]\) of degree increasing type such that \(X(\underline {a}/d) = 0\) and ≤= . Make , and public.

Choose a finite subset \(\Lambda \subset (\mathbb {Z}_{\geq 0})^{n}\) such that \(\# \left \{\sum \underline {i} \mid \underline {i} \in \Lambda \right \} = \# \Lambda \) .

Let \(\underline {k} = (k_{1},\ldots,k_{n})\) be the maximal element of . For \(\underline {i} \in \Lambda ^{\prime } := \Lambda \smallsetminus \{\underline {0}, \underline {k} \}\) , choose random non-zero integers \(c_{\underline {i}}\) .

$$\frac{c_{\underline{k}}\underline{a}^{\underline{k}} + c_{\underline{0}}d^{w}}{d^{w}} = - \frac{\sum_{\underline{i} \in \Lambda^{\prime}}c_{\underline{i}}\underline{a}^{\underline{i}}d^{w^{\prime} - \sum \underline{i}}}{d^{w^{\prime}}}, $$
$$ c_{\underline{k}}\underline{a}^{\underline{k}} + c_{\underline{0}}d^{w} = - \sum_{\underline{i} \in \Lambda^{\prime}}c_{\underline{i}}\underline{a}^{\underline{i}}d^{w - \sum \underline{i}}. $$
(4)
$$X := \sum_{\underline{i} \in \Lambda}c_{\underline{i}}\underline{x}^{\underline{i}}. $$

The condition on Λ (step 1 above) means that X is of degree increasing type. The equation ( 4 ) means that \(X(\underline {a}/d) = 0\) .

The Military Wife and Mom

Parenting and motherhood in the midst of military life

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Ever dream of a morning where you are drinking a cup of coffee, checking e-mail, paying a few bills, and you are without interruption and it’s quiet?! This is no dream. Teaching children to play independently, while you get some business done around the house, is totally possible, and you can start from birth! Today I’m continuing on with my Babywise Basics series and talking about Independent Playtime (If you missed my previous Babywise Basics posts on Why We Chose Babywise and How to Sleep-Train , be sure to check them out).

The idea of children playing alone comes most commonly from the book Babywise II . Using the Babywise method or not, anyone can teach their children this really awesome, mutually beneficial skill with a little bit of parental diligence.

1. Independent playtime defined.

Independent play time (IPT) is a daily scheduled time when your child plays alone, without parents or other siblings around. You choose the time of the day and with which toys your child will play. Occurring at approximately the same time every day, IPT typically takes place in a pack ‘n play or play yard for younger babies/ toddler. Older toddlers and children will transition from the play yard to their rooms and have IPT in their room or other room of the house.

Mental focusing skills : Playpen time helps a child develop the ability to concentrate on an object and apply knowledge to the activity at hand without distraction.

Sustained attention span: The interval during which a child can concentrate on a single object or activity will gradually improve and lengthen over time.

Creativity: Absolute freedom eliminates the need for creative thinking, while boundaries facilitate creativity. The child will learn to find enjoyment out of what’s available to them. The child will create meaningful new methods and interpretations during play.

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By OlympicTalk Jul 7, 2018, 2:12 PM EDT

Top-ranked Simona Halep became the ninth woman in the top 10 seeds to be upset in the first week of Wimbledon, falling6-3, 4-6, 7-5 to Hsieh Su-wei of Taiwan in the third round on Saturday.

Simona Halep Hsieh Su-wei

More: Olympics

Cuban boxer with two Olympic gold medals leaves national team Austria pulls out of 2026 Winter Olympic bidding Shelby Houlihan stars, Noah Lyles outduels Michael Norman in Lausanne (video)

No. 7 Karolina Pliskova is the only top-10 seed left in the women’s draw heading to the round of 16. The clear favorite is No. 25 seed Serena Williams , seeking her eighth Wimbledon title and first Grand Slam title since Sept. 1 childbirth.

Karolina Pliskova Serena Williams

Williams gets fellow mom and Russian qualifier Evgeniya Rodina in the fourth round on Monday and would not play a seed before the semifinals. She is the only Grand Slam singles winner left in the bottom half of the draw.

Evgeniya Rodina

The top half is headlined by No. 12 Jelena Ostapenko , the 2017 French Open champion, and two-time Grand Slam winner and 11th seed Angelique Kerber , who beat No. 18 Naomi Osaka 6-2, 6-4 on Saturday.

Jelena Ostapenko Angelique Kerber Naomi Osaka

Halep, who won her first Grand Slam at the French Open last month, made the Wimbledon quarterfinals the last two years and the semifinals in 2014.

Rafael Nadal had no such problems, and guaranteed he will stay No. 1 in the men’s rankings as he reached the fourth round with a 6-1, 6-2, 6-4 victory over 19-year-old Australian Alex de Minaur .

Tipple Hill Winery Vineyard Music
Saturday, October 21, 2017 - 7:00pm to 9:30pm
Tipple Hill Winery Vineyard

Enjoy live music by Phil Vandel at Tipple Hill Winery Vineyard on October 21.

Sunday Football Tailgate Party
Sunday, October 22, 2017 - 11:00am to 5:00pm
Jowler Creek Vineyard Winery

It's finally football season! Don't be sad if you're not going to the big game in person. Cheer on your favorite team at Jowler Creek Vineyard Winery. Watch the game and enjoy grilled brats and fun, traditional tailgating games like redneck golf, washers, yard Yahtzee and Giant Jenga. Red Arrowhead Sangria as well as wine and beer, by the glass or bottle, will be available for purchase. Free event. No reservations required to join in the fun.

Crowns Crayons Grown-up Coloring Event
Sunday, October 22, 2017 - 12:00pm to 5:00pm
Weston Wine Company
Stone Hill Winery Oktoberfest
Sunday, October 22, 2017 - 12:00pm to 5:00pm
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Thursday, October 26, 2017 - 7:00pm to 9:00pm
Jowler Creek Vineyard Winery

Looking for a fun activity for date night, girls night out or just a fun night with friends? Sip on some wine and paint! The $39/person cost includes all the supplies you need for the painting, a fun step-by-step lesson by local art instructor, Angie Carmack, delicious snacks and a beverage (alcoholic or non-alcoholic) of your choice. Reservations and pre-payment are required. Call (816) 858-5528 to reserve your spot.

Grill Your Own Dinner Night
Friday, October 27, 2017 - 7:00pm to 9:00pm
Jowler Creek Vineyard Winery

Bring your favorite meat to Jowler Creek Vineyard Winery. The winerywill provide the fire, utensils and seasonings for you to grill your selection to perfection. The winery will have an assortment of delicious sides and gourmet S'more packetsavailable to purchase, as well as their award-winning wines, beer and non-alcoholicbeverages. Free event.

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Saturday, October 28, 2017 - 10:00am to 4:30pm
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Saturday, October 28, 2017 - 11:00am to Sunday, October 29, 2017 - 5:00pm
Weston Wine Company

Looking for a festive treat for all your goblins andghouls this year! Give them a delectable Reese’s Frankenstein cupcake!They’re only $1.99/each, $10.99 for a 6-pack or $19.99/dozen! Feel free tocall us at (816) 386-2345 to pre-purchase your cupcakes as they’re onlyavailable while supplies last. Event URL: http://www.westonwinecompany.com

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